Messages from 2005
These are the messages distributed to the Banach list during 2005.
From alspach at www.math.okstate.edu Fri Jan 7 09:15:01 2005
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Date: Fri, 7 Jan 2005 09:15:00 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200501071515.j07FF0B1021657 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Dmitry B. Rokhlin
Status: R
This is an announcement for the paper "The Kreps-Yan theorem for
$L^\infty$" by Dmitry B. Rokhlin.
Abstract: We prove the following version of the Kreps-Yan theorem. For
any norm closed convex cone $C\subset L^\infty$ such that $C\cap
L_+^\infty=\{0\}$ and $C\supset -L_+^\infty$, there exists a strictly
positive continuous linear functional, whose restriction on $C$ is
non-positive. The proof uses some tools from convex analysis in contrast
to the case of a weakly Lindel\"of Banach space, where such approach is
not needed.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46E30; 46B40
Remarks: 8 pages
The source file(s), rok_KY.TEX: 18051 bytes, is(are) stored in gzipped
form as 0412551.gz with size 7kb. The corresponding postcript file has
gzipped size 45kb.
Submitted from: rokhlin at math.rsu.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0412551
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http://arXiv.org/abs/math.FA/0412551
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From alspach at www.math.okstate.edu Fri Jan 7 09:16:53 2005
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Date: Fri, 7 Jan 2005 09:16:53 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200501071516.j07FGrix021745 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Biagio Ricceri
Status: R
This is an announcement for the paper "Covering dimension and nonlinear
equations" by Biagio Ricceri.
Abstract: Theorem: Let X and Y be two Banach spaces, Phi: X to Y a
continuous, linear, surjective operator, and Psi: X to Y a completely
continuous operator with bounded range. Then, one has dim{x in X :
Phi(x)=Psi(x)} >= dim(Phi^{-1}(0)). Here dim denotes the covering
dimension.
Archive classification: Functional Analysis
Mathematics Subject Classification: 47J05, 47H10
Citation: RIMS Kokyuroku 1031, 97-100 (1998)
Remarks: 3 pages
The source file(s), paam-15.tex: 7189 bytes, is(are) stored in gzipped
form as 0412563.gz with size 3kb. The corresponding postcript file has
gzipped size 26kb.
Submitted from: elliott at mail.mathatlas.yorku.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0412563
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http://arXiv.org/abs/math.FA/0412563
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From alspach at www.math.okstate.edu Fri Jan 7 09:17:40 2005
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Date: Fri, 7 Jan 2005 09:17:40 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200501071517.j07FHec2021806 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Biagio Ricceri
Status: R
This is an announcement for the paper "Some research perspectives in
nonlinear functional analysis" by Biagio Ricceri.
Abstract: The object of this lecture is to propose a series of conjectures
and problems in different fields of analysis. They have been formulated
with the aim of introducing some innovative methods in the study of
classical topics, as open mappings, fixed points, critical points,
global minima, control theory.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46N10, 47H10
Citation: Semin. Fixed Point Theory Cluj-Napoca 3, 99-110 (2002)
Remarks: 13 pages
The source file(s), idec-62.tex: 26131 bytes, is(are) stored in gzipped
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Submitted from: elliott at mail.mathatlas.yorku.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0412564
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http://arXiv.org/abs/math.FA/0412564
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From alspach at www.math.okstate.edu Fri Jan 7 09:21:17 2005
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Fri, 7 Jan 2005 09:21:16 -0600
Date: Fri, 7 Jan 2005 09:21:16 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200501071521.j07FLGTI021899 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Magdalena Musat
Status: R
This is an announcement for the paper "On the operator space UMD property
for noncommutative Lp-spaces" by Magdalena Musat.
Abstract: We study the operator space UMD property, introduced by
Pisier in the context of noncommutative vector-valued Lp-spaces. It is
unknown whether the property is independent of p in this setting. We
prove that for 1<p,q<\infty, the Schatten q-classes Sq are OUMDp. The
proof relies on properties of the Haagerup tensor product and complex
interpolation. Using ultraproduct techniques, we extend this result to
a large class of noncommutative Lq-spaces. Namely, we show that if M
is a QWEP von Neumann algebra (i.e., a quotient of a C^*-algebra with
Lance's weak expectation property) equipped with a normal, faithful
tracial state \tau, then Lq(M,\tau) is OUMDp for 1<p,q<\infty.
Archive classification: Operator Algebras; Functional Analysis; Probability
Mathematics Subject Classification: 46L52, 47L25 (Primary) 60G46
(Secondary)
Remarks: 30 pages
The source file(s), OUMDLP.TEX: 120786 bytes, is(are) stored in gzipped
form as 0501033.gz with size 33kb. The corresponding postcript file has
gzipped size 135kb.
Submitted from: mmusat at math.ucsd.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.OA/0501033
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http://arXiv.org/abs/math.OA/0501033
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From alspach at www.math.okstate.edu Mon Jan 10 08:20:23 2005
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Date: Mon, 10 Jan 2005 08:20:23 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200501101420.j0AEKNUG027875 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by W. T. Gowers
Status: R
This is an announcement for the paper "An infinite Ramsey theorem and
some Banach-space dichotomies" by W. T. Gowers.
Abstract: A problem of Banach asks whether every infinite-dimensional
Banach space which is isomorphic to all its infinite-dimensional subspaces
must be isomorphic to a separable Hilbert space. In this paper we prove a
result of a Ramsey-theoretic nature which implies an interesting dichotomy
for subspaces of Banach spaces. Combined with a result of Komorowski and
Tomczak-Jaegermann, this gives a positive answer to Banach's problem. We
then generalize the Ramsey-theoretic result and deduce a further dichotomy
for Banach spaces with an unconditional basis.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B20 (Primary) 03E02, 03E15, 05D10,
46B03 (Secondary)
Citation: Ann. of Math. (2), Vol. 156 (2002), no. 3, 797--833
Remarks: 37 pages, published version
The source file(s), ArxivGowers.tex: 109202 bytes, amltd2004.sty:
33983 bytes, is(are) stored in gzipped form as 0501105.tar.gz with size
42kb. The corresponding postcript file has gzipped size 112kb.
Submitted from: wtg10 at dpmms.cam.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0501105
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http://arXiv.org/abs/math.FA/0501105
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From alspach at www.math.okstate.edu Thu Jan 13 12:16:04 2005
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Date: Thu, 13 Jan 2005 12:16:04 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200501131816.j0DIG4fs021237 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by A.G. Smirnov and M.A. Soloviev
Status: R
This is an announcement for the paper "On kernel theorems for Frechet
and DF spaces" by A.G. Smirnov and M.A. Soloviev.
Abstract: A convenient technique for calculating completed topological
tensor products of functional Frechet or DF spaces is developed. The
general construction is applied to proving kernel theorems for a wide
class of spaces of smooth and entire analytic functions.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46A32; 46E10; 46A04
Remarks: 10 pages
The source file(s), kernel1.tex: 40782 bytes, is(are) stored in gzipped
form as 0501187.gz with size 12kb. The corresponding postcript file has
gzipped size 64kb.
Submitted from: smirnov at lpi.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0501187
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From banach-bounces at math.okstate.edu Sun Jan 16 22:11:43 2005
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From: Dale Alspach <alspach at math.okstate.edu>
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Subject: [Banach] Conference at Kent State
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Status: R
A conference on Infinite Dimensional Analysis (IDAKent2005) will be held
February 9-13, 2005, in honor of Richard Aron and Sean Dineen.
The Conference web page is http://www.math.kent.edu/idaconf2005.html.
We invite everyone, even those who cannot attend the conference, to
send, as image files (preferably as JPG files), photographs of yourself
with Richard and/or Sean, indicating the place and the year when they were
taken. These photos will be displayed on the Conference web page.
In order to arrange the schedule of the Conference we need to know who
plans to give talks. The deadline for sending us the title and abstract
of your talk is Friday, January 28 (and remember that everyone,
absolutely
everyone, is welcome whether or not he/she plans on giving a talk!)
On the web page (LODGING), you can find information about many hotels from
which to choose. To reserve hotel rooms at the IDA conference rate,
please make your reservations through Misty Tackett. To do this, please
(1) DOWNLOAD THE FORM FOR ROOM RESERVATIONS AS A TXT FILE,
(2) FILL IN THIS FORM, and
(3) E-MAIL THE FORM BACK TO Ms. Tackett at mtackett at math.kent.edu
As an alternative, you can DOWNLOAD THE FORM FOR ROOM RESERVATIONS
AS A PDF FILE, FILL IN THIS FORM, AND FAX IT BACK TO Ms. Tackett
(++ 1 330 672 2209). Note that Adobe Reader 6 does not allow you to save
what you write on the pdf, but you can print the modified pdf file.
Reservations not made through Ms. Tackett will not be available at a
reduced rate. The deadline for room reservations is Friday January
21st,
2005.
Please let us know your arrival and departure times if you plan to fly
to this area. We will arrange for a shuttle to take you to and from
the airport when you are arriving or departing from the airports
(Akron-Canton=CAK, Cleveland-Hopkins=CLE). To do this, we will need your
detailed travel information. This will help us ensure that you are not
missed at the airport if your flight happens to be delayed when
arriving. By giving us your accurate departure information, we
can help you be on time when going home as well! Please send the
following information to garcia at math.kent.edu as soon as possible. On
the web page you can also find in ARRIVALS AND DEPARTURES the following
information that you can copy and paste into your email.
Your Name:
Arrival Information
Airport (Cleveland or Akron):
Flight Number:
Arrival Date and Time:
Departure Information
Airport (Cleveland or Akron):
Flight Number:
Arrival Date and Time:
By now a lot of people have confirmed that they will attend. Among them:
María Acosta, University of Granada, Spain
Raymundo Alencar, Instituto Tecnologico da
Aeronautica, Sao Jose dos Campos, Brazil
Richard Aron, Kent State University, USA
Rajappa K. Asthagiri, Miami University, Middletown, USA
Juan Bés, Bowling Green State University, USA
Klaus Bierstedt, University of Paderborn, Germany
Geraldo Botelho, Federal University of Uberlândia, Brazil
Christopher Boyd, University College Dublin, Ireland
Bernardo Cascales, University of Murcia, Spain
Jesús Castillo, University of Extremadura, Badajoz, Spain
Yun Sung Choi, POSTECH, Pohang, Korea
Joe Cima, The University of North Carolina at Chapel Hill, USA
Antonio Roberto da Silva, Federal University of Rio de Janeiro, Brazil
Andreas Defant, University of Oldenburg, Germany
Joe Diestel, Kent State University, USA
Verónica Dimant, University of San Andrés, Victoria, Argentina
Seán Dineen, University College Dublin, Ireland
Patrick Dowling, Miami University, Oxford, USA
Maite Fernández-Unzueta, CIMAT, Guadalajara, Mexico
Jesús Ferrer, University of Valencia, Spain
Catherine Finet, University of Mons, Belgium
Pablo Galindo, University of Valencia, Spain
Domingo García, University of Valencia, Spain
Bogdan Grecu, Tallaght Institute of Technology, Ireland
André Hallack, Federal University of Juiz de Fora, Brazil
Lawrence A. Harris, University of Kentucky, USA
Tatsuhiro Honda, Ariake National College of Technology, Fukuoka, Japan
Remo Hügli, University College Dublin, Ireland
Hans Jarchow, University of Zurich, Switzerland
Jesús Jaramillo, University Complutense of Madrid, Spain
Ana Kaminska, The University of Memphis, USA
Padraig Kirwan, Waterford Institue of Technology, Ireland
Maciej Klimek, Uppsala University, Sweden
Istvan Kovacs, Case Western Reserve University, Cleveland, USA
László Lempert, Purdue University, USA
Chris Lennard, University of Pittsburgh, USA
Fernando León, University of Cadiz, Spain
Mikael Lindström, Åbo Akademi University, Finland
José L. G. Llavona, University Complutense of Madrid, Spain
Lilian Lourenço, University of São Paulo, Brazil
Michael Mackey, University College Dublin, Ireland
Manuel Maestre, University of Valencia, Spain
Miguel Martín, University of Granada, Spain
Félix Martínez Giménez, Technical University of Valencia, Spain
Mieczyslaw Mastylo, Adam Mickiewicz University, Poznan, Poland
Vicente Montesinos Santalucia, Technical University of Valencia, Spain
Luiza Moraes, Federal University of Rio de Janeiro, Brazil
Lawrence Narici, Saint Johns University, New York, USA
José Orihuela, University of Murcia, Spain
Imre Patyi, Georgia State University, USA
Aleksander Pelczynski, Institute of Mathematics, Polish
Academy of Sciences, Poland
Daniel Pellegrino, Federal University of Campina Grande, Brazil
David Pérez, University Rey Juan Carlos of Madrid, Spain
Alfredo Peris Manguillot, Technical University of Valencia, Spain
Wieslaw Plesniak, Jagiellonian University, Krakow, Poland
Lucas Quarta, University of Mons, Belgium
María José Rivera, Technical University of Valencia, Spain
Pilar Rueda, University of Valencia, Spain
Raymond Ryan, University of Galway, Ireland
Jean Schmets, University of Liège, Belgium
Pablo Sevilla, University of Valencia, Spain
Emily Sprague, University of Wisconsin, USA
Kondagunta Sundaresan, Cleveland State University, USA
Ciaran Taylor, Tallaght Institute of Technology, Ireland
Richard Timoney, Trinity College Dublin, Ireland
Andrew Tonge, Kent State University, USA
Milena Venkova, University College Dublin, Ireland
Daniela Vieira, State University of Campinas, Brazil
Ignacio Villanueva, University Complutense of Madrid, Spain
Dietmar Vogt, University of Wuppertal, Germany
Andriy Zagorodnyuk, Inst. for Applied Problems of Mechanics and
Mathematics, Ukraine
Ignacio Zalduendo, Universidad Torcuato di Tella, Buenos Aires,
Argentina
We hope that you too will be a participant in Kent during February 9 -
13, 2005!
The organizing committee,
Yun Sung Choi, Domingo García, Manolo Maestre, Andrew Tonge, Nacho
Zalduendo.
_______________________________________________
Banach mailing list
Banach at math.okstate.edu
http://mail.math.okstate.edu:8080/mailman/listinfo/banach
From banach-bounces at math.okstate.edu Tue Jan 25 12:52:57 2005
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Date: Tue, 25 Jan 2005 12:52:51 -0600
From: Dale Alspach <alspach at math.okstate.edu>
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Subject: [Banach] Conference on Banach spaces and their Applications in
Analysis
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Status: R
Conference Announcement:
``Banach spaces and their applications in Analysis'',
in honor of Nigel Kalton's 60th birthday,
to be held May 22-27, 2006 at Miami University in
Oxford, Ohio (which is about 30 miles from Cincinnati,
Ohio).
We plan to emphasize the following themes:
-- Nonlinear theory (Lipschitz classifications of Banach and
metric spaces and related topics),
-- Isomorphic theory of Banach spaces including connections with
combinatorics and set theory,
-- Algebraic and homological methods in Banach spaces,
-- Approximation theory and algorithms in Banach spaces
(greedy algorithms, interpolation etc.),
-- Functional calculus and applications to Partial Differential
Equations.
The following people have agreed to be principal speakers at the conference:
Yuri Brudnyi (Technion - Israel Institute of Technology, Israel)
Jesús M. F. Castillo (University of Extremadura, Spain)
Marianna Csörnyei (University College, London, UK)
Stephen Dilworth (University of South Carolina)
Gilles Godefroy (Universitè Paris VI, France)
William B. Johnson (Texas A&M University)
Joram Lindenstrauss (Hebrew University, Israel)
Assaf Naor (Microsoft Research)
Edward Odell (University of Texas)
Aleksander Pelczynski (Polish Academy of Sciences, Poland)
David Preiss (University College, London, UK)
Gideon Schechtman (Weizmann Institute of Science, Israel)
Thomas Schlumprecht (Texas A&M University)
Vladimir Temlyakov (University of South Carolina)
Roman Vershynin (University of California - Davis)
Lutz Weis (Universität Karlsruhe, Germany)
Przemyslaw Wojtaszczyk (Warsaw University, Poland)
More information about the conference, its location, registration,
accommodations and a printable poster are available at the website:
http://www.users.muohio.edu/randrib/bsaa2006.html
Please direct any questions to either of the organizers at randrib at muohio.edu
or randrin at muohio.edu
Sincerely yours,
Beata Randrianantoanina
Narcisse Randrianantoanina.
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From: J R Partington <pmt6jrp at maths.leeds.ac.uk>
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Subject: [Banach] Lectureship in Analysis at Leeds
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Status: R
There is a lectureship in Analysis (a permanent position) currently
advertised at the School of Mathematics, University of Leeds, U.K. The
closing date for applications is March 1st 2005.
Further details are available by following the link from
http://wwwnotes2.leeds.ac.uk/jobs/unijob.nsf/Academic?OpenView
Details of the Functional Analysis group at Leeds can be found at
http://maths.leeds.ac.uk/pure/analysis/index.html
Informal enquiries can be directed to Professors M.J. Wilson (Chairman
of the School), mike at maths.leeds.ac.uk, J.C. Wood (Head of Pure
Mathematics), j.c.wood at leeds.ac.uk, or J.R. Partington,
j.r.partington at leeds.ac.uk.
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From alspach at www.math.okstate.edu Wed Jan 26 07:18:51 2005
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Date: Wed, 26 Jan 2005 07:18:51 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200501261318.j0QDIphI011019 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Rafal Latal and Krzysztof Oleszkiewicz
Status: R
This is an announcement for the paper "Small ball probability estimates
in terms of width" by Rafal Latal and Krzysztof Oleszkiewicz.
Abstract: A certain inequality conjectured by Vershynin is studied. It
is proved that for any $n$-dimensional symmetric convex body $K$ with
inradius $w$ and $\gamma_{n}(K) \leq 1/2$ there is $\gamma_{n}(sK)
\leq (2s)^{w^{2}/4}\gamma_{n}(K)$ for any $s \in [0,1]$. Some natural
corollaries are deduced. Another conjecture of Vershynin is proved to
be false.
Archive classification: Probability; Functional Analysis
Mathematics Subject Classification: 60G15, 60E15
Remarks: 10 pages
The source file(s), , is(are) stored in gzipped form as with size . The
corresponding postcript file has gzipped size .
Submitted from: rlatala at mimuw.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.PR/0501268
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http://arXiv.org/abs/math.PR/0501268
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From alspach at www.math.okstate.edu Wed Jan 26 07:20:03 2005
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Date: Wed, 26 Jan 2005 07:20:03 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200501261320.j0QDK392011109 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Sasha Sodin
Status: R
This is an announcement for the paper "Tail-sensitive Gaussian asymptotics
for marginals of concentrated measures in high dimension" by Sasha
Sodin.
Abstract: If the Euclidean norm is strongly concentrated with respect
to a measure, the average distribution of an average marginal of this
measure has Gaussian asymptotics that captures tail behaviour. If the
marginals of the measure have exponential moments, Gaussian asymptotics
for the distribution of the average marginal implies Gaussian asymptotics
for the distribution of most individual marginals. We show applications
to measures of geometric origin.
Archive classification: Metric Geometry; Functional Analysis
Remarks: 29 pages
The source file(s), all3.tex: 62865 bytes, is(are) stored in gzipped
form as 0501382.gz with size 19kb. The corresponding postcript file has
gzipped size 96kb.
Submitted from: a_sodin at hotmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.MG/0501382
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From alspach at www.math.okstate.edu Fri Feb 4 13:13:56 2005
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Date: Fri, 4 Feb 2005 13:13:55 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200502041913.j14JDtn8018520 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Harald Hanche-Olsen
Status: R
This is an announcement for the paper "On the uniform convexity of L^p"
by Harald Hanche-Olsen.
Abstract: We present a short, direct proof of the uniform convexity of
L^p spaces for 1<p<\infty.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46E30
The source file(s), uc2.tex: 7706 bytes, is(are) stored in gzipped form
as 0502021.gz with size 3kb. The corresponding postcript file has gzipped
size 26kb.
Submitted from: hanche at math.ntnu.no
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0502021
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From alspach at www.math.okstate.edu Fri Feb 4 13:15:52 2005
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Date: Fri, 4 Feb 2005 13:15:52 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200502041915.j14JFqej018607 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Valentin Ferenczi
Status: R
This is an announcement for the paper "Minimality, homogeneity and
topological 0-1 laws for subspaces of a Banach space" by Valentin
Ferenczi.
Abstract: If a Banach space is saturated with basic sequences whose linear
span embeds into the linear span of any subsequence, then it contains
a minimal subspace. It follows that any Banach space is either ergodic
or contains a minimal subspace.
If $X$ is a Banach space with a Schauder basis, the relation $E_0$
is Borel reducible to permutative equivalence between normalized
block-sequences of $X$, or $X$ is $c_0$-saturated or $l_p$-saturated for
some $1 \leq p <+\infty$.
For a Banach space $X$ with an (unconditional) basis, topological 0-1 law
type dichotomies are stated for block-subspaces of $X$ as well
as for subspaces of $X$ with a successive FDD on its basis. A
uniformity principle for properties of block-sequences, results about
block-homogeneity, and a possible method to construct a Banach space
with an unconditional basis, which has a complemented subspace without
an unconditional basis, are deduced.
Archive classification: Functional Analysis; Combinatorics
Mathematics Subject Classification: 46B03; 46B15
The source file(s), ferenczitopolaw.tex: 93769 bytes, is(are) stored in
gzipped form as 0502054.gz with size 26kb. The corresponding postcript
file has gzipped size 99kb.
Submitted from: ferenczi at ccr.jussieu.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0502054
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From alspach at www.math.okstate.edu Thu Feb 10 08:22:26 2005
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Date: Thu, 10 Feb 2005 08:22:26 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200502101422.j1AEMQl2020821 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jesus M. F. Castillo, Yolanda Moreno and Jesus Suarez
Status: R
This is an announcement for the paper "On Lindenstrauss-Pelczynski spaces"
by Jesus M. F. Castillo, Yolanda Moreno and Jesus Suarez.
Abstract: In this work we shall be concerned with some stability
aspects of the classical problem of extension of $C(K)$-valued
operators. We introduce the class $\mathscr{LP}$ of Banach spaces of
Lindenstrauss-Pe\l czy\'{n}sky type as those such that every operator
from a subspace of $c_0$ into them can be extended to $c_0$. We show that
all $\mathscr{LP}$-spaces are of type $\mathcal L_\infty$ but not the
converse. Moreover, $\mathcal L_\infty$-spaces will be characterized as
those spaces $E$ such that $E$-valued operators from $w^*(l_1,c_0)$-closed
subspaces of $l_1$ extend to $l_1$. Complemented subspaces of $C(K)$ and
separably injective spaces are subclasses of $\mathscr{LP}$-spaces and
we show that the former does not contain the latter. It is established
that $\mathcal L_\infty$-spaces not containing $l_1$ are quotients of
$\mathscr{LP}$-spaces, while $\mathcal L_\infty$-spaces not containing
$c_0$, quotients of an $\mathscr{LP}$-space by a separably injective
space and twisted sums of $\mathscr{LP}$-spaces are $\mathscr{LP}$-spaces.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B03; 46M99; 46B07
The source file(s), CastilloMorenoLP.tex: 49873 bytes, is(are) stored in
gzipped form as 0502081.gz with size 15kb. The corresponding postcript
file has gzipped size 72kb.
Submitted from: castillo at unex.es
The paper may be downloaded from the archive by web browser from URL
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From alspach at www.math.okstate.edu Wed Feb 16 08:15:36 2005
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Date: Wed, 16 Feb 2005 08:15:35 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200502161415.j1GEFZQJ024774 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Mark Rudelson and Roman Vershynin
Status: R
This is an announcement for the paper "Geometric approach to error
correcting codes and reconstruction of signals" by Mark Rudelson and
Roman Vershynin.
Abstract: We develop an approach through geometric functional analysis to
error correcting codes and to reconstruction of signals from few linear
measurements. An error correcting code encodes an n-letter word x into
an m-letter word y in such a way that x can be decoded correctly when
any r letters of y are corrupted. We prove that most linear orthogonal
transformations Q from R^n into R^m form efficient and robust robust
error correcting codes over reals. The decoder (which corrects the
corrupted components of y) is the metric projection onto the range of Q
in the L_1 norm. An equivalent problem arises in signal processing: how
to reconstruct a signal that belongs to a small class from few linear
measurements? We prove that for most sets of Gaussian measurements,
all signals of small support can be exactly reconstructed by the L_1
norm minimization. This is a substantial improvement of recent results
of Donoho and of Candes and Tao. An equivalent problem in combinatorial
geometry is the existence of a polytope with fixed number of facets and
maximal number of lower-dimensional facets. We prove that most sections
of the cube form such polytopes.
Archive classification: Functional Analysis; Combinatorics
Mathematics Subject Classification: 46B07; 94B75, 68P30, 52B05
Remarks: 17 pages, 3 figures
The source file(s), ecc.tex: 50560 bytes, ecc1.eps: 4526 bytes, ecc2.eps:
17097 bytes, ecc3.eps: 4645 bytes, is(are) stored in gzipped form as
0502299.tar.gz with size 23kb. The corresponding postcript file has
gzipped size 84kb.
Submitted from: vershynin at math.ucdavis.edu
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From alspach at www.math.okstate.edu Wed Feb 16 08:16:18 2005
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Date: Wed, 16 Feb 2005 08:16:18 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200502161416.j1GEGINu024832 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Hun Hee Lee
Status: R
This is an announcement for the paper "OH-type and OH-cotype of operator
spaces and completely summing maps" by Hun Hee Lee.
Abstract: The definition and basic properties of OH-type and OH-cotype
of operator spaces are given. We prove that every bounded linear map
from C(K) into OH-cotype q (2<= q < infinity) space (including most
of commutative L_q-spaces) for a compact set K satisfies completely
(q,2)-summing property, a noncommutative analogue of absolutely
(q,2)-summing property. At the end of this paper, we observe that
``OH-cotype 2" is equivalent to the previous definition of ``OH-cotype 2"
of G. Pisier.
Archive classification: Functional Analysis; Operator Algebras
Remarks: 17 pages
The source file(s), OH-typecotype.tex: 46265 bytes, is(are) stored in
gzipped form as 0502302.gz with size 13kb. The corresponding postcript
file has gzipped size 80kb.
Submitted from: hunmada at hanmail.net
The paper may be downloaded from the archive by web browser from URL
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From alspach at www.math.okstate.edu Wed Feb 16 08:17:05 2005
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Date: Wed, 16 Feb 2005 08:17:05 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200502161417.j1GEH5ju024890 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Hun Hee Lee
Status: R
This is an announcement for the paper "Eigenvalues of completely nuclear
maps and completely bounded projection constants" by Hun Hee Lee.
Abstract: We investigate the distribution of eigenvalues of completely
nuclear maps on an operator space. We prove that eigenvalues of
completely nuclear maps are square-summable in general and summable if
the underlying operator space is Hilbertian and homogeneous. Conversely,
if eigenvalues are summable for all completely nuclear maps, then
every finite dimensional subspace of the underlying operator space is
uniformly completely complemented. As an application we consider an
estimate of completely bounded projection constants of $n$-dimensional
operator spaces.
Archive classification: Functional Analysis; Operator Algebras
Remarks: 10 pages
The source file(s), EigenComNuclear.tex: 27465 bytes, is(are) stored in
gzipped form as 0502335.gz with size 9kb. The corresponding postcript
file has gzipped size 55kb.
Submitted from: hunmada at hanmail.net
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0502335
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From alspach at www.math.okstate.edu Thu Feb 17 07:10:08 2005
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Date: Thu, 17 Feb 2005 07:10:08 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200502171310.j1HDA8Xq002941 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Hun Hee Lee
Status: R
This is an announcement for the paper "Weak OH-type 2 and weak OH-cotype
2 of operator spaces" by Hun Hee Lee.
Abstract: Recently, OH-type and OH-cotype of operator spaces, an operator
space version of type and cotype, were introduced and investigated by the
author. In this paper we define weak OH-type 2 (resp. weak OH-cotype 2) of
operator spaces, which lies strictly between OH-type 2 (resp. OH-cotype 2)
and OH-type $p$ for all $1 \leq p < 2$. (resp. OH-cotype $q$ for all $2<
q <= \infty$) This is an analogue of weak type 2 and weak cotype 2 in
Banach space case, so we develop analogous theory focusing on the local
properties of spaces with such conditions.
Archive classification: Functional Analysis; Operator Algebras
Remarks: 21 pages
The source file(s), WeakOH.tex: 55124 bytes, is(are) stored in gzipped
form as 0502337.gz with size 15kb. The corresponding postcript file has
gzipped size 85kb.
Submitted from: hunmada at hanmail.net
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0502337
or
http://arXiv.org/abs/math.FA/0502337
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uget 0502337
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From alspach at www.math.okstate.edu Wed Mar 9 09:11:17 2005
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Date: Wed, 9 Mar 2005 09:11:16 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200503091511.j29FBGsh013215 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Miguel Martin, Javier Meri and Rafael Paya
Status: R
This is an announcement for the paper "On the intrinsic and the spatial
numerical range" by Miguel Martin, Javier Meri and Rafael Paya.
Abstract: For a bounded function $f$ from the unit sphere of a closed
subspace $X$ of a Banach space $Y$, we study when the closed convex
hull of its spatial numerical range $W(f)$ is equal to its intrinsic
numerical range $V(f)$. We show that for every infinite-dimensional
Banach space $X$ there is a superspace $Y$ and a bounded linear operator
$T:X\longrightarrow Y$ such that $\ecc W(T)\neq V(T)$. We also show
that, up to renormig, for every non-reflexive Banach space $Y$, one can
find a closed subspace $X$ and a bounded linear operator $T\in L(X,Y)$
such that $\ecc W(T)\neq V(T)$.
Finally, we introduce a sufficient condition for the closed convex
hull of the spatial numerical range to be equal to the intrinsic numerical
range, which we call the Bishop-Phelps-Bollobas property, and which is
weaker than the uniform smoothness and the finite-dimensionality. We
characterize strong subdifferentiability and uniform smoothness in terms
of this property.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B20; 47A12
Remarks: 12 pages
The source file(s), MartinMeriPaya.tex: 40725 bytes, is(are) stored in
gzipped form as 0503076.gz with size 13kb. The corresponding postcript
file has gzipped size 70kb.
Submitted from: mmartins at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0503076
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From alspach at www.math.okstate.edu Tue Mar 22 09:03:49 2005
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Tue, 22 Mar 2005 09:03:48 -0600
Date: Tue, 22 Mar 2005 09:03:48 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200503221503.j2MF3m2A020304 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by V.Yaskin
Status: R
This is an announcement for the paper "A solution to the lower dimensional
Busemann-Petty problem in the hyperbolic space" by V.Yaskin.
Abstract: The lower dimensional Busemann-Petty problem asks whether
origin symmetric convex bodies in $\mathbb{R}^n$ with smaller volume
of all $k$-dimensional sections necessarily have smaller volume. As
proved by Bourgain and Zhang, the answer to this question is negative
if $k>3$. The problem is still open for $k=2,3$. In this article we
formulate and completely solve the lower dimensional Busemann-Petty
problem in the hyperbolic space $\mathbb{H}^n$.
Archive classification: Functional Analysis; Metric Geometry
Mathematics Subject Classification: 52A55, 52A20, 46B20
Remarks: 12 pages, 2 figures
The source file(s), LDHBP.tex: 70816 bytes, pic04.eps: 9457 bytes,
pic06.eps: 9542 bytes, is(are) stored in gzipped form as 0503289.tar.gz
with size 25kb. The corresponding postcript file has gzipped size 59kb.
Submitted from: yaskinv at math.missouri.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0503289
or
http://arXiv.org/abs/math.FA/0503289
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From alspach at www.math.okstate.edu Tue Mar 22 09:04:31 2005
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Date: Tue, 22 Mar 2005 09:04:31 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200503221504.j2MF4VfF020362 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by V.Yaskin and M.Yaskina
Status: R
This is an announcement for the paper "Centroids and comparison of
volumes" by V.Yaskin and M.Yaskina.
Abstract: For $-1<p<1$ we introduce the concept of a polar $p$-centroid
body ${\Gamma^*_p K}$ of a star body $K$. We consider the question of
whether ${\Gamma^*_p K}\subset {\Gamma^*_p L}$ implies $\mathrm{vol}(L)\le
\mathrm{vol}(K).$ Our results extend the studies by Lutwak in the case
$p=1$ and Grinberg, Zhang in the case $p> 1$.
Archive classification: Functional Analysis
Mathematics Subject Classification: 52Axx
Remarks: 18 pages
The source file(s), centr.tex: 51970 bytes, is(are) stored in gzipped
form as 0503290.gz with size 13kb. The corresponding postcript file has
gzipped size 71kb.
Submitted from: yaskinv at math.missouri.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0503290
or
http://arXiv.org/abs/math.FA/0503290
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uget 0503290
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From alspach at www.math.okstate.edu Wed Mar 23 08:18:49 2005
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Date: Wed, 23 Mar 2005 08:18:49 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200503231418.j2NEInwc030699 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Mark Rudelson and Roman Vershynin
Status: R
This is an announcement for the paper "Sampling from large matrices:
an approach through geometric functional analysis" by Mark Rudelson
and Roman Vershynin.
Abstract: We study random submatrices of a large matrix A. We show how to
approximately compute A from its random submatrix. This improves known
algorithms for computing low-rank approximations of large matrices. We
also estimate norms of random submatrices of A. This yields an improved
approximation algorithm for all MAX-2CSP problems (which includes MAX-CUT
and other graph problems). Our results are essentially dimension-free;
the picture is only controlled by the norms of the matrix and not by
its size or rank. We use methods of Probability in Banach spaces, in
particular the law of large numbers for random operators.
Archive classification: Functional Analysis; Numerical Analysis
Mathematics Subject Classification: 15A60, 68W20, 15A18
The source file(s), rv-random-submatrices.tex: 50699 bytes, is(are)
stored in gzipped form as 0503442.gz with size 16kb. The corresponding
postcript file has gzipped size 82kb.
Submitted from: vershynin at math.ucdavis.edu
The paper may be downloaded from the archive by web browser from URL
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From alspach at www.math.okstate.edu Tue Mar 29 12:17:36 2005
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Date: Tue, 29 Mar 2005 12:17:36 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200503291817.j2TIHapg006350 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Madjid Mirzavaziri and Mohammad Sal Moslehian
Status: R
This is an announcement for the paper "Parallelogram norm" by Madjid
Mirzavaziri and Mohammad Sal Moslehian.
Abstract: Replacing the triangle inequality by \|x+y\|^2\leq 2(\|x\|^2 +
\|y\|^2) in the definition of norm we obtain the notion of parallelogram
norm. We establish that every parallelogram norm is a norm in the
usual sense.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B20; 46C05
Remarks: 3 pages
The source file(s), Paral1.tex: 4582 bytes, is(are) stored in gzipped
form as 0503616.gz with size 2kb. The corresponding postcript file has
gzipped size 27kb.
Submitted from: msalm at math.um.ac.ir
The paper may be downloaded from the archive by web browser from URL
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or
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Status: R
Le volume 12 de la collection "Cours Specialises" est a votre disposition.
INTRODUCTION A L'ETUDE DES ESPACES DE BANACH
ANALYSE ET PROBABILITES
Daniel Li, Herve Queffelec
xxiv+627 pages
Ce livre est consacre a l'etude des espaces de Banach, en mettant l'accent
sur les liens avec l'Analyse classique, l'Analyse Harmonique, et les
Probabilites. Seules des connaissances usuelles d'Analyse Fonctionnelle de
niveau Maitrise sont requises, l'etude etant prise a son debut. Elle est
progressivement developpee de facon approfondie, presentant plusieurs
resultats fondamentaux obtenus dans la periode 1950--2000: Theoreme de
Grothendieck, Theoreme de Dvoretzky, Theoreme de dichotomie de Rosenthal,
Theoreme de dichotomie de Gowers, etc., avec certaines de leurs applications.
This book is devoted to the study of Banach spaces, with emphasis on the
connections with classical Analysis, Harmonic Analysis and Probability
Theory. It can be tackled by beginning graduates: the study is taken at its
beginning, and then worked out thoroughly, presenting several fundamental
results which were obtained during the period 1950--2000: Grothendieck's
Theorem, Dvoretzky's Theorem, Rosenthal's dichotomy Theorem, Gowers's
dichotomy Theorem, etc., with some of their applications.
Prix public (pour chaque volume) : 72 euro + frais de port (France : 5
euro, Europe : 6 euro, Hors Europe : 7 euro)
Prix membre (pour chaque volume) : 51 euro + frais de port (France : 5
euro, Europe : 6 euro, Hors Europe : 7 euro)
Vous pouvez vous procurer ces volumes en le commandant a la cellule de
diffusion de Marseille :
Maison de la SMF, BP 67, 13274 Marseille cedex 09,
Tel : (33) 04 91 26 74 64, Fax : (33) 04 91 41 17 57,
email : smf at smf.univ-mrs.fr,
url : http://smf.emath.fr/, ou en passant le chercher au secretariat de la
SMF a Paris (IHP, 11 rue Pierre et Marie Curie 75005 Paris).
Vous pouvez aussi passer directement votre commande par l'intermediaire du
serveur a l'adresse suivante : http://smf.emath.fr/
Daniel Li
Université d'Artois
Laboratoire de Mathématiques de Lens (LML)
Faculté des Sciences Jean Perrin
rue Jean Souvraz, SP 18
62307 LENS Cedex
Tel +33 (0)3 21 79 17 22
Fax +33 (0)3 21 79 17 29
daniel.li at euler.univ-artois.fr
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From alspach at www.math.okstate.edu Fri Apr 1 08:27:10 2005
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Date: Fri, 1 Apr 2005 08:27:10 -0600
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200504011427.j31ERAWa006098 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Guillaume Aubrun and Stanislaw J. Szarek
Status: R
This is an announcement for the paper "Tensor products of convex sets
and the volume of separable states on N qudits" by Guillaume Aubrun
and Stanislaw J. Szarek.
Abstract: This note deals with estimating the volume of the set of
separable mixed quantum states when the dimension of the state space
grows to infinity. This has been studied recently for qubits; here we
consider larger particles. We also show that the partial transpose
criterion becomes weaker when the dimension increases, and that the
lower bound $6^{-N/2}$ on the (Hilbert-Schmidt) inradius of the set of
separable states on $N$ qubits obtained recently by Gurvits and Barnum
is essentially optimal. We employ standard tools of classical convexity,
high-dimensional probability and geometry of Banach spaces; one relatively
new point is a formal introduction of the concept of projective tensor
products of convex bodies, and an initial study of this concept.
PACS numbers: 03.65.Ud,03.67.-a,03.65.Db,02.40.Ft,02.50.Cw MSC-class:
46B28, 47B10, 47L05, 52A38, 81P68
Archive classification: Quantum Physics; Functional Analysis
Remarks: 14 pages
The source file(s), , is(are) stored in gzipped form as with size . The
corresponding postcript file has gzipped size .
Submitted from: szarek at cwru.edu
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http://front.math.ucdavis.edu/quant-ph/0503221
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From alspach at www.math.okstate.edu Tue Apr 5 07:58:24 2005
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Date: Tue, 5 Apr 2005 07:58:24 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200504051258.j35CwOJE021163 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by S. S. Kutateladze
Status: R
This is an announcement for the paper "On Grothendieck subspaces" by
S. S. Kutateladze.
Abstract: The modulus of an order bounded functional on a Riesz space
is the sum of a pair of Riesz homomorphisms if and only if the kernel of
this functional is a Grothendieck subspace of the ambient Riesz space. An
operator version of this fact is given.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46 B 42
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form as 0504046.gz with size 2kb. The corresponding postcript file has
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Submitted from: sskut at member.ams.org
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From alspach at www.math.okstate.edu Mon Apr 11 12:36:07 2005
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Date: Mon, 11 Apr 2005 12:36:06 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200504111736.j3BHa6bo026362 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Piotr Puchala
Status: R
This is an announcement for the paper "Continuous version of the Choquet
Integral Reperesentation Theorem" by Piotr Puchala.
Abstract: The Choquet - Bishop - de Leeuw theorem states that each element
of a compact convex subset of a locally convex topological Hausdorff space
is a barycenter of a probability measure supported by the set of extreme
points of that set. By the Edgar - Mankiewicz result this remains true
for nonempty closed bounded and convex set provided it has Radon - Nikodym
property. In the paper it is shown, that Choquet - type theorem holds also
for "moving" sets: they are values of a certain multifunction. Namely, the
existence of a suitable weak* continuous family of probability measures
"almost representing" points of such sets is proven. Both compact and
noncompact cases are considered. The continuous versions of the Krein -
Milman theorem are obtained as corollaries.
Archive classification: Functional Analysis
Mathematics Subject Classification: 54C60; 54C65; 46A55; 46B22
Citation: Studia Math. 168 (1), 2005, 15-24
Remarks: 9 pages, minor historical, editorial and bibliographical changes;
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0405217
or
http://arXiv.org/abs/math.FA/0405217
or by email in unzipped form by transmitting an empty message with
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uget 0405217
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From banach-bounces at math.okstate.edu Mon Apr 11 17:17:55 2005
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Date: Mon, 11 Apr 2005 16:27:37 -0500 (CDT)
From: Bill Johnson <johnson at math.tamu.edu>
To: banach at math.okstate.edu
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Subject: [Banach] Workshop at A&M
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Status: R
Workshop in Linear Analysis and Probability
Department of Mathematics
Texas A&M University
Summer 2005
The Summer 2005 session of the Workshop in Linear Analysis and
Probability at Texas A&M University will be in session from July 5
until August 9. For information about the Workshop, consult the Workshop
Home Page, URL
http://www.math.tamu.edu/research/workshops/linanalysis/
The Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held
August 5-7. This year SUMIRFAS is dedicated to Haskell P. Rosenthal on the
occasion of his retirement from the University of Texas at Austin.
Haskell was one of the original organizers of UTAMIRFAS, the forerunner of
SUMIRFAS. There will be a banquet in Haskell's honor on August 5. The
usual SUMIRFAS dinner will be on August 6.
Alvaro Arias, Edward Odell, and Thomas Schlumprecht are organizing a
Haskell Fest Mini-Conference that will take place on August 4 and the
morning of August 5.
Ronald Douglas and Ciprian Foias are organizing a Mini-Conference on
"Invariant and Hyperinvariant Subspaces - Old and New" that will take
place August 8-9. This Mini-Conference is in honor of Carl Pearcy on the
occasion of his 70th birthday. On August 8 there will be a banquet in
Carl's honor.
The Workshop is supported in part by grants from the National Science
Foundation (NSF). Minorities, women, graduate students, and young
researchers are especially encouraged to attend.
For logistical support, including requests for support, please contact
Mary Chapman (mary at math.tamu.edu). For more information on the Workshop
itself, please contact William Johnson (johnson at math.tamu.edu), David
Larson (larson at math.tamu.edu), Gilles Pisier (pisier at math.tamu.edu), or
Joel Zinn (jzinn at math.tamu.edu).
For information about the Haskell Fest Mini-Conference, please contact
Alvaro Arias (aarias at math.du.edu), Edward Odell
(odell at mail.ma.utexas.edu), or Thomas Schlumprecht
(schlump at math.tamu.edu).
For information about the Mini-Conference on Invariant Subspaces, please
contact Ronald Douglas (rdouglas at math.tamu.edu).
_______________________________________________
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From alspach at www.math.okstate.edu Tue Apr 12 11:36:10 2005
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Date: Tue, 12 Apr 2005 11:36:10 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200504121636.j3CGaAMr004968 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Joan E. Hart and Kenneth Kunen
Status: R
This is an announcement for the paper "Inverse limits and function
algebras" by Joan E. Hart and Kenneth Kunen.
Abstract: Assuming Jensen's principle diamond, there is a compact
Hausdorff space X which is hereditarily Lindelof, hereditarily separable,
and connected, such that no closed subspace of X is both perfect and
totally disconnected. The Proper Forcing Axiom implies that there is
no such space. The diamond example also fails to satisfy the CSWP
(the complex version of the Stone-Weierstrass Theorem). This space
cannot contain the two earlier examples of failure of the CSWP, which
were totally disconnected -- specifically, the Cantor set (W. Rudin)
and beta N (Hoffman and Singer).
Archive classification: General Topology; Functional Analysis
Mathematics Subject Classification: 54D05; 46J10
Remarks: 16 pages
The source file(s), invlim.tex: 45668 bytes, is(are) stored in gzipped
form as 0504228.gz with size 15kb. The corresponding postcript file has
gzipped size 80kb.
Submitted from: kunen at math.wisc.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.GN/0504214
or
http://arXiv.org/abs/math.GN/0504214
or by email in unzipped form by transmitting an empty message with
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uget 0504214
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From banach-bounces at math.okstate.edu Tue Apr 12 13:51:55 2005
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Subject: [Banach] Incorrect paper number for Inverse Limits and Function
Algebras
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Status: R
The announcement for the paper Inverse Limits and Function Algebras
contains incorrect links such as
http://front.math.ucdavis.edu/math.GN/0504228
The correct links are
http://front.math.ucdavis.edu/math.GN/0504214
http://arXiv.org/abs/math.GN/0504214
Dale Alspach
_______________________________________________
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From alspach at www.math.okstate.edu Thu Apr 14 10:41:44 2005
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Date: Thu, 14 Apr 2005 10:41:43 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200504141541.j3EFfhxL026048 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Marius Junge
Status: R
This is an announcement for the paper "Operator spaces and Araki-Woods
factors" by Marius Junge.
Abstract: We show that the operator Hilbert space OH introduced by Pisier
embeds into the predual of the hyerfinite III1 factor. The main new tool
is a Khintchine type inequality for the generators of the CAR algebra
with respect to a quasi-free state. Our approach yields a Khintchine
type inequality for the q-gaussian variables for all values q between
-1 and 1. These results are closely related to recent results of Pisier
and Shlyakhtenko in the free case.
Archive classification: Operator Algebras; Functional Analysis
Mathematics Subject Classification: 46L53, 47L25
The source file(s), carcomp.tex: 194521 bytes, is(are) stored in gzipped
form as 0504255.gz with size 59kb. The corresponding postcript file has
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Submitted from: junge at math.uiuc.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.OA/0504255
or
http://arXiv.org/abs/math.OA/0504255
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From alspach at www.math.okstate.edu Fri Apr 15 15:56:48 2005
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Date: Fri, 15 Apr 2005 15:56:48 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200504152056.j3FKumpk006133 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Florence Lancien, Beata Randrianantoanina, and Eric Ricard
Status: R
This is an announcement for the paper "On contractive projections in Hardy
spaces" by Florence Lancien, Beata Randrianantoanina, and Eric Ricard.
Abstract: We prove a conjecture of Wojtaszczyk that for $1\leq p<\infty$,
$p\neq 2$, $H_p(\mathbbT)$ does not admit any norm one projections
with dimension of the range finite and bigger than 1. This implies in
particular that for $1\leq p<\infty$, $p\ne 2$, $H_p$ does not admit a
Schauder basis with constant one.
Archive classification: Functional Analysis; Complex Variables
Remarks: 9 pages, to appear in Studia Mathematica
The source file(s), hardy9.tex: 30622 bytes, is(are) stored in gzipped
form as 0504294.gz with size 11kb. The corresponding postcript file has
gzipped size 57kb.
Submitted from: randrib at muohio.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0504294
or
http://arXiv.org/abs/math.FA/0504294
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From banach-bounces at math.okstate.edu Wed Apr 20 08:07:21 2005
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Cc:
Subject: [Banach] Vladimir Gurariy
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Status: R
It is with great sadness that the Department of Mathematical Sciences
of Kent State University announces the passing of Dr. Vladimir Gurariy
on Sunday, April 17, 2005. For many years, Vladimir was a colleague and
great friend to all. We remember his brilliance in so many areas, his
kindness and generosity, his sense of fun, and his humanity.
_______________________________________________
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From alspach at www.math.okstate.edu Mon Apr 25 11:49:51 2005
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Date: Mon, 25 Apr 2005 11:49:51 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200504251649.j3PGnpe7029177 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jan van Neerven and Mark Veraar
Status: R
This is an announcement for the paper "On the action of Lipschitz
functions on vector-valued random sums" by Jan van Neerven and Mark
Veraar.
Abstract: Let $X$ be a Banach space and let $(\xi_j)_{j\ge 1}$ be an
i.i.d. sequence of symmetric random variables with finite moments of
all orders. We prove that the following assertions are equivalent:
(1). There exists a constant $K$ such that $$ \Bigl(\E\Big\|\sum_{j=1}^n
\xi_j f(x_j)\Big\|^2\Bigr)^{\frac12} \leq K \n f\n_{\rm Lip}
\Bigl(\E\Big\|\sum_{j=1}^n \xi_j x_j\Big\|^2\Bigr)^{\frac12} $$ for
all Lipschitz functions $f:X\to X$ satisfying $f(0)=0$ and all finite
sequences $x_1,\dots,x_n$ in $X$.
(2). $X$ is isomorphic to a Hilbert space.
Archive classification: Functional Analysis; Probability
Mathematics Subject Classification: 46C15, 46B09, 47B10
Remarks: 8 pages, to appear in Archiv der Mathematik (Basel)
The source file(s), lipschitzA.tex: 27762 bytes, is(are) stored in
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Submitted from: m.c.veraar at math.tudelft.nl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0504452
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http://arXiv.org/abs/math.FA/0504452
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From alspach at www.math.okstate.edu Wed May 11 08:07:46 2005
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200505111307.j4BD7k3g003601 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Marianne Morillon
Status: R
This is an announcement for the paper "A new proof of James' sup theorem"
by Marianne Morillon.
Abstract: We provide a new proof of James' sup theorem for (non
necessarily separable) Banach spaces. One of the ingredients is the
following generalization of a theorem of Hagler and Johnson (1977) :
"If a normed space $E$ does not contain any asymptotically isometric copy
of $\ell^1(\IN)$, then every bounded sequence of $E'$ has a normalized
block sequence pointwise converging to $0$".
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B ; 03E25
Report Number: ERMIT-MM-07jan2005
The source file(s), envoi.bbl: 2807 bytes, envoi.tex: 35905 bytes,
icone-ermit.eps: 24310 bytes, is(are) stored in gzipped form as
0505176.tar.gz with size 19kb. The corresponding postcript file has
gzipped size 69kb.
Submitted from: Marianne.Morillon at univ-reunion.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0505176
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From alspach at www.math.okstate.edu Wed May 11 08:18:35 2005
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Date: Wed, 11 May 2005 08:18:35 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200505111318.j4BDIZgb003765 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Denny H. Leung and Wee-Kee Tang
Status: R
This is an announcement for the paper "Extension of functions with small
oscillation" by Denny H. Leung and Wee-Kee Tang.
Abstract: A classical theorem of Kuratowski says that every Baire one
function on a G_\delta subspace of a Polish (= separable completely
metrizable) space X can be extended to a Baire one function on X. Kechris
and Louveau introduced a finer gradation of Baire one functions into
small Baire classes. A Baire one function f is assigned into a class
in this heirarchy depending on its oscillation index \beta(f). We
prove a refinement of Kuratowski's theorem: if Y is a subspace
of a metric space X and f is a real-valued function on Y such that
\beta_{Y}(f)<\omega^{\alpha}, \alpha < \omega_1, then f has an extension
F onto X so that \beta_X(F)is not more than \omega^{\alpha}. We also
show that if f is a continuous real valued function on Y, then f has an
extension F onto X so that \beta_{X}(F)is not more than 3. An example
is constructed to show that this result is optimal.
Archive classification: Classical Analysis and ODEs; Functional Analysis
Mathematics Subject Classification: 26A21; 03E15, 54C30
The source file(s), DLeungWTangBaire1Ext.tex: 47118 bytes, is(are)
stored in gzipped form as 0505168.gz with size 13kb. The corresponding
postcript file has gzipped size 71kb.
Submitted from: wktang at nie.edu.sg
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.CA/0505168
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From alspach at www.math.okstate.edu Tue May 17 06:41:30 2005
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Date: Tue, 17 May 2005 06:41:30 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200505171141.j4HBfUIH007313 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by M.Yaskina
Status: R
This is an announcement for the paper "Non-intersection bodies all of
whose central sections are intersection bodies" by M.Yaskina.
Abstract: We construct symmetric convex bodies that are not intersection
bodies, but all of their central hyperplane sections are intersection
bodies. This result extends the studies by Weil in the case of zonoids
and by Neyman in the case of subspaces of $L_p$.
Archive classification: Functional Analysis; Metric Geometry
Mathematics Subject Classification: 52A20, 52A21, 46B20
Remarks: 10 pages
The source file(s), inters8.tex: 33376 bytes, is(are) stored in gzipped
form as 0505277.gz with size 10kb. The corresponding postcript file has
gzipped size 54kb.
Submitted from: yaskinv at math.missouri.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0505277
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From alspach at www.math.okstate.edu Tue May 17 06:42:45 2005
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Date: Tue, 17 May 2005 06:42:44 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200505171142.j4HBgiAL007371 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Felix Cabello Sanchez, Jesus M. F. Castillo and Pier Luigi Papini
Status: R
This is an announcement for the paper "Seven views on approximate
convexity and the geometry of K-spaces" by Felix Cabello Sanchez, Jesus
M. F. Castillo and Pier Luigi Papini.
Abstract: As in Hokusai's series of paintings "Thirty six views of
mount Fuji" in which mount Fuji's is sometimes scarcely visible, the
central topic of this paper is the geometry of $K$-spaces although in
some of the seven views presented $K$-spaces are not easily visible. We
study the interplay between the behaviour of approximately convex (and
approximately affine) functions on the unit ball of a Banach space and
the geometry of Banach K-spaces.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B20; 52A05; 42A65; 26B25
Remarks: 2 figures
The source file(s), ccp.tex: 61322 bytes, cubo.eps: 19389 bytes,
kominek.eps: 82795 bytes, is(are) stored in gzipped form as 0505291.tar.gz
with size 38kb. The corresponding postcript file has gzipped size 119kb.
Submitted from: castillo at unex.es
The paper may be downloaded from the archive by web browser from URL
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From alspach at www.math.okstate.edu Tue May 17 06:46:31 2005
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Date: Tue, 17 May 2005 06:46:31 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200505171146.j4HBkVsN007463 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Eric Ricard and Quanhua Xu
Status: R
This is an announcement for the paper "Khintchine type inequalities for
reduced free products and applications" by Eric Ricard and Quanhua Xu.
Abstract: We prove Khintchine type inequalities for words of a fixed
length in a reduced free product of $C^*$-algebras (or von Neumann
algebras). These inequalities imply that the natural projection from a
reduced free product onto the subspace generated by the words of a fixed
length $d$ is completely bounded with norm depending linearly on $d$. We
then apply these results to various approximation properties on reduced
free products. As a first application, we give a quick proof of Dykema's
theorem on the stability of exactness under the reduced free product for
$C^*$-algebras. We next study the stability of the completely contractive
approximation property (CCAP) under reduced free product. Our first result
in this direction is that a reduced free product of finite dimensional
$C^*$-algebras has the CCAP. The second one asserts that a von Neumann
reduced free product of injective von Neumann algebras has the weak-$*$
CCAP. In the case of group $C^*$-algebras, we show that a free product
of weakly amenable groups with constant 1 is weakly amenable.
Archive classification: Operator Algebras; Functional Analysis
Mathematics Subject Classification: Primary 46L09, 46L54; Secondary
47L07, 47L25
The source file(s), kpl.tex: 94450 bytes, is(are) stored in gzipped
form as 0505302.gz with size 30kb. The corresponding postcript file has
gzipped size 136kb.
Submitted from: qx at math.univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.OA/0505302
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http://arXiv.org/abs/math.OA/0505302
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From alspach at www.math.okstate.edu Tue May 17 06:49:00 2005
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Tue, 17 May 2005 06:48:59 -0500
Date: Tue, 17 May 2005 06:48:59 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200505171148.j4HBmxI5007522 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Teresa Martinez, Jose L. Torrea and Quanhua Xu
Status: R
This is an announcement for the paper "Vector-valued
Littlewood-Paley-Stein theory for semigroups" by Teresa Martinez, Jose
L. Torrea and Quanhua Xu.
Abstract: We develop a generalized Littlewood-Paley theory for semigroups
acting on $L^p$-spaces of functions with values in uniformly convex or
smooth Banach spaces. We characterize, in the vector-valued setting,
the validity of the one-sided inequalities concerning the generalized
Littlewood-Paley-Stein $g$-function associated with a subordinated
Poisson symmetric diffusion semigroup by the martingale cotype and type
properties of the underlying Banach space. We show that in the case of
the usual Poisson semigroup and the Poisson semigroup subordinated to
the Ornstein-Uhlenbeck semigroup on ${\mathbb R}^n$, this general theory
becomes more satisfactory (and easier to be handled) in virtue of the
theory of vector-valued Calder\'on-Zygmund singular integral operators.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B20; 42B25, 42A61
Remarks: To appear in Adv. Math
The source file(s), lpsII.tex: 111765 bytes, is(are) stored in gzipped
form as 0505303.gz with size 31kb. The corresponding postcript file has
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Submitted from: qx at math.univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0505303
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From alspach at www.math.okstate.edu Tue May 17 06:50:45 2005
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Date: Tue, 17 May 2005 06:50:45 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200505171150.j4HBojdv007622 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Quanhua Xu
Status: R
This is an announcement for the paper "A description of
$\big(C_p[L_p(M)],\; R_p[L_p(M)]\big)_\theta$" by Quanhua Xu.
Abstract: We give a simple explicit description of the norm in the
complex interpolation space $(C_p[L_p(M)],\; R_p[L_p(M)])_\theta$ for
any von Neumann algebra $M$ and any $1\le p\le\infty$.
Archive classification: Functional Analysis; Operator Algebras
Mathematics Subject Classification: Primary 46M35 and 46L51; Secondary
46L07
Remarks: To appear in Proc. Edinburgh Math. Soc
The source file(s), interpCR.tex: 33942 bytes, is(are) stored in gzipped
form as 0505305.gz with size 11kb. The corresponding postcript file has
gzipped size 61kb.
Submitted from: qx at math.univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0505305
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From alspach at www.math.okstate.edu Tue May 17 06:52:14 2005
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Date: Tue, 17 May 2005 06:52:13 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200505171152.j4HBqDwR007680 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Quanhua Xu
Status: R
This is an announcement for the paper "Operator space Grothendieck
inequalities for noncommutative $L_p$-spaces" by Quanhua Xu.
Abstract: We prove the operator space Grothendieck inequality for bilinear
forms on subspaces of noncommutative $L_p$-spaces with $2<p<\infty$. One
of our results states that given a map $u: E\to F^*$, where $E,
F\subset L_p(M)$ ($2<p<\infty$, $M$ being a von Neumann algebra),
$u$ is completely bounded iff $u$ factors through a direct sum of a
$p$-column space and a $p$-row space. We also obtain several operator
space versions of the classical little Grothendieck inequality for maps
defined on a subspace of a noncommutative $L_p$-space ($2<p<\infty$)
with values in a $q$-column space for every $q\in [p', p]$ ($p'$ being
the index conjugate to $p$). These results are the $L_p$-space analogues
of the recent works on the operator space Grothendieck theorems by
Pisier and Shlyakhtenko. The key ingredient of our arguments is some
Khintchine type inequalities for Shlyakhtenko's generalized circular
systems. One of our main tools is a Haagerup type tensor norm, which turns
out particularly fruitful when applied to subspaces of noncommutative
$L_p$-spaces ($2<p<\infty$). In particular, we show that the norm dual
to this tensor norm, when restricted to subspaces of noncommutative
$L_p$-spaces, is equal to the factorization norm through a $p$-row space.
Archive classification: Functional Analysis; Operator Algebras
Mathematics Subject Classification: Primary 46L07; Secondary 46L50
Remarks: To appear in Duke Math. J
The source file(s), gro.tex: 127607 bytes, is(are) stored in gzipped
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The paper may be downloaded from the archive by web browser from URL
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From alspach at www.math.okstate.edu Tue May 17 06:53:44 2005
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Tue, 17 May 2005 06:53:43 -0500
Date: Tue, 17 May 2005 06:53:43 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200505171153.j4HBrh9X007738 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Quanhua Xu
Status: R
This is an announcement for the paper "Embedding of $C_q$ and $R_q$
into noncommutative $L_p$-spaces, $1\le p<q\le 2$" by Quanhua Xu.
Abstract: We prove that a quotient of subspace of $C_p\oplus_pR_p$
($1\le p<2$) embeds completely isomorphically into a noncommutative
$L_p$-space, where $C_p$ and $R_p$ are respectively the $p$-column and
$p$-row Hilbertian operator spaces. We also represent $C_q$ and $R_q$
($p<q\le2$) as quotients of subspaces of $C_p\oplus_pR_p$. Consequently,
$C_q$ and $R_q$ embed completely isomorphically into a noncommutative
$L_p(M)$. We further show that the underlying von Neumann algebra $M$
cannot be semifinite.
Archive classification: Functional Analysis; Operator Algebras
Mathematics Subject Classification: Primary 46L07; Secondary 47L25
The source file(s), embed.tex: 63829 bytes, is(are) stored in gzipped
form as 0505307.gz with size 19kb. The corresponding postcript file has
gzipped size 96kb.
Submitted from: qx at math.univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0505307
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http://arXiv.org/abs/math.FA/0505307
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From alspach at www.math.okstate.edu Tue May 17 06:58:12 2005
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Date: Tue, 17 May 2005 06:58:11 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200505171158.j4HBwBIF007865 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Marius Junge and Quanhua Xu
Status: R
This is an announcement for the paper "On the best constants in some
non-commutative martingale inequalities" by Marius Junge and Quanhua Xu.
Abstract: We determine the optimal orders for the best constants in the
non-commutative Burkholder-Gundy, Doob and Stein inequalities obtained
recently in the non-commutative martingale theory.
Archive classification: Operator Algebras, Functional Analysis; Probability
Mathematics Subject Classification: 46L53, 46L51
Citation: Bull. London Math. Soc. 37:243--253, 2005
The source file(s), constant.revised.tex: 33956 bytes, is(are) stored in
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The paper may be downloaded from the archive by web browser from URL
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From alspach at www.math.okstate.edu Fri May 20 09:35:43 2005
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Date: Fri, 20 May 2005 09:35:43 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200505201435.j4KEZhJl006706 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by D. Rokhlin and W. Schachermayer
Status: R
This is an announcement for the paper "A note on lower bounds of
martingale measure densities" by D. Rokhlin and W. Schachermayer.
Abstract: For a given element $f\in L^1$ and a convex cone $C\subset
L^\infty$, $C\cap L^\infty_+=\{0\}$ we give necessary and sufficient
conditions for the existence of an element $g\ge f$ lying in the polar of
$C$. This polar is taken in $(L^\infty)^*$ and in $L^1$. In the context of
mathematical finance the main result concerns the existence of martingale
measures, whose densities are bounded from below by prescribed random
variable.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46E30
Remarks: 9 pages
The source file(s), SCH_P4.TEX: 22410 bytes, is(are) stored in gzipped
form as 0505411.gz with size 8kb. The corresponding postcript file has
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Submitted from: rokhlin at math.rsu.ru
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From alspach at www.math.okstate.edu Sun Jun 5 11:38:12 2005
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Date: Sun, 5 Jun 2005 11:38:12 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200506051638.j55GcCNU020141 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Rubin Boris
Status: R
This is an announcement for the paper "The generalized Busemann-Petty
problem with weights" by Rubin Boris.
Abstract: The generalized Busemann-Petty problem asks whether
origin-symmetric convex bodies with lower-dimensional smaller sections
necessarily have smaller volume. We study the weighted version of
this problem corresponding to the physical situation when bodies are
endowed with mass distribution and the relevant sections are measured
with attenuation.
Archive classification: Functional Analysis
Mathematics Subject Classification: 52A38; 44A12
Remarks: 12 pages
The source file(s), sol1.tex: 32080 bytes, is(are) stored in gzipped
form as 0505666.gz with size 11kb. The corresponding postcript file has
gzipped size 57kb.
Submitted from: borisr at math.lsu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0505666
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From alspach at www.math.okstate.edu Sun Jun 5 11:39:52 2005
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Date: Sun, 5 Jun 2005 11:39:52 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200506051639.j55GdqZR020199 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Koenraad M.R. Audenaert
Status: R
This is an announcement for the paper "A norm compression inequality
for block partitioned positive semidefinite matrices" by Koenraad
M.R. Audenaert.
Abstract: Let $A$ be a positive semidefinite matrix, block partitioned as
$$ A=\twomat{B}{C}{C^*}{D}, $$ where $B$ and $D$ are square blocks. We
prove the following inequalities for the Schatten $q$-norm $||.||_q$,
which are sharp when the blocks are of size at least $2\times2$: $$
||A||_q^q \le (2^q-2) ||C||_q^q + ||B||_q^q+||D||_q^q, \quad 1\le q\le 2,
$$ and $$ ||A||_q^q \ge (2^q-2) ||C||_q^q + ||B||_q^q+||D||_q^q, \quad
2\le q. $$ These bounds can be extended to symmetric partitionings into
larger numbers of blocks, at the expense of no longer being sharp: $$
||A||_q^q \le \sum_{i} ||A_{ii}||_q^q + (2^q-2) \sum_{i<j} ||A_{ij}||_q^q,
\quad 1\le q\le 2, $$ and $$ ||A||_q^q \ge \sum_{i} ||A_{ii}||_q^q +
(2^q-2) \sum_{i<j} ||A_{ij}||_q^q, \quad 2\le q. $$
Archive classification: Functional Analysis
Mathematics Subject Classification: 15A60
Remarks: 24 pages
The source file(s), normcompr_v3.tex: 50189 bytes, is(are) stored in
gzipped form as 0505680.gz with size 16kb. The corresponding postcript
file has gzipped size 79kb.
Submitted from: kauden at imperial.ac.uk
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From alspach at math.okstate.edu Wed Jun 15 10:22:18 2005
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X-Mailer: exmh version 2.7.2 01/07/2005 with nmh-1.1-RC3
To: alspach at www.math.okstate.edu
Subject: [Banach] Abstract of a paper by Piotr W. Nowak (fwd)
Mime-Version: 1.0
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Date: Wed, 15 Jun 2005 10:22:10 -0500
From: Dale Alspach <alspach at math.okstate.edu>
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Status: R
------- Forwarded Message
Date: Fri, 10 Jun 2005 09:22:24 -0500
From: Dale Alspach <alspach at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
cc:
Subject: [Banach] Abstract of a paper by Piotr W. Nowak
This is an announcement for the paper "A metric space not
quasi-isometrically embeddable into any uniformly convex Banach space"
by Piotr W. Nowak.
Abstract: We construct a locally finite graph and a bounded geometry
metric space which do not admit a quasi-isometric embedding into any
uniformly convex Banach space. Connections with the geometry of $c_0$
and superreflexivity are discussed.
Archive classification: Metric Geometry; Functional Analysis
Remarks: 6 pages, 2 figures
The source file(s),
Quasi-isometricnon-embeddabilityintouniformlyconvexBanachspaces.tex:
18532 byt, figuramain.eps: 7608 bytes, figure1.eps: 3766 bytes, is(are)
stored in gzipped form as 0506178.tar.gz with size 9kb. The corresponding
postcript file has gzipped size 44kb.
Submitted from: pnowak at math.vanderbilt.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.MG/0506178
or
http://arXiv.org/abs/math.MG/0506178
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From alspach at www.math.okstate.edu Wed Jun 15 09:43:25 2005
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Date: Wed, 15 Jun 2005 09:43:25 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200506151443.j5FEhP7P018252 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Ngai-Ching Wong
Status: R
This is an announcement for the paper "The triangle of operators,
topologies, bornologies" by Ngai-Ching Wong.
Abstract: This paper discusses two common techniques in functional
analysis: the topological method and the bornological method. In
terms of Pietsch's operator ideals, we establish the equivalence
of the notions of operators, topologies and bornologies. The
approaches in the study of locally convex spaces of Grothendieck
(via Banach space operators), Randtke (via continuous seminorms)
and Hogbe-Nlend (via convex bounded sets) are compared.
Archive classification: Functional Analysis; Operator Algebras
Mathematics Subject Classification: 47L20, 46A03, 46A11, 46A17
Remarks: 33 pages
The source file(s), triangle05_ArXiV.tex: 98877 bytes, is(are)
stored in gzipped form as 0506183.gz with size 27kb. The corresponding
postcript file has gzipped size 124kb.
Submitted from: wong at math.nsysu.edu.tw
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0506183
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From alspach at www.math.okstate.edu Wed Jun 15 09:44:37 2005
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Date: Wed, 15 Jun 2005 09:44:37 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200506151444.j5FEibOB018297 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Shahar Mendelson, Alain Pajor and Nicole Tomczak-Jaegermann
Status: R
This is an announcement for the paper "Reconstruction and subgaussian
operators" by Shahar Mendelson, Alain Pajor and Nicole Tomczak-Jaegermann.
Abstract: We present a randomized method to approximate any vector
$v$ from some set $T \subset \R^n$. The data one is given is the
set $T$, and $k$ scalar products $(\inr{X_i,v})_{i=1}^k$, where
$(X_i)_{i=1}^k$ are i.i.d. isotropic subgaussian random vectors in
$\R^n$, and $k \ll n$. We show that with high probability, any $y
\in T$ for which $(\inr{X_i,y})_{i=1}^k$ is close to the data vector
$(\inr{X_i,v})_{i=1}^k$ will be a good approximation of $v$, and
that the degree of approximation is determined by a natural geometric
parameter associated with the set $T$.
We also investigate a random method to identify exactly any vector
which has
a relatively short support using linear subgaussian measurements
as above. It turns out that our analysis, when applied to
$\{-1,1\}$-valued vectors with i.i.d, symmetric entries, yields new
information on the geometry of faces of random
$\{-1,1\}$-polytope; we show that a $k$-dimensional random
$\{-1,1\}$-polytope with $n$ vertices is $m$-neighborly for very
large $m\le {ck/\log (c' n/k)}$. The proofs are based on new
estimates on the behavior of the empirical
process $\sup_{f \in F} \left|k^{-1}\sum_{i=1}^k f^2(X_i) -\E f^2
\right|$ when $F$ is a subset of the $L_2$ sphere. The estimates
are given in terms of the $\gamma_2$ functional with respect to the
$\psi_2$ metric on $F$, and hold both in exponential probability
and in expectation.
Archive classification: Functional Analysis; Probability
Mathematics Subject Classification: 46B07, 47B06, 41A45; 94B75,
52B05
Remarks: 31 pages; no figures; submitted
The source file(s), MPT_subgaussian.tex: 75209 bytes, is(are) stored
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postcript file has gzipped size 106kb.
Submitted from: alain.pajor at univ-mlv.fr
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URL
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From alspach at www.math.okstate.edu Thu Jun 16 13:49:46 2005
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Date: Thu, 16 Jun 2005 13:49:46 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200506161849.j5GInkqB030248 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Manor Mendel, Assaf Naor
Status: R
This is an announcement for the paper "Scaled Enflo type is equivalent
to Rademacher type" by Manor Mendel and Assaf Naor.
Abstract: We introduce the notion of scaled Enflo type of a metric
space, and show that for Banach spaces, scaled Enflo type p is
equivalent to Rademacher type p.
Archive classification: Functional Analysis; Metric Geometry
Mathematics Subject Classification: 46B20; 51F99
Remarks: 5 pages
The source file(s), enflo-rademacher.tex: 16927 bytes, is(are)
stored in gzipped form as 0506215.gz with size 5kb. The corresponding
postcript file has gzipped size 47kb.
Submitted from: mendelma at gmail.com
The paper may be downloaded from the archive by web browser from
URL
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From alspach at www.math.okstate.edu Thu Jun 16 13:50:40 2005
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Date: Thu, 16 Jun 2005 13:50:40 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200506161850.j5GIoeDb030293 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by George Androulakis
Status: R
This is an announcement for the paper "A new method of constructing
invariant subspaces" by George Androulakis.
Abstract: The method of compatible sequences is introduced in order
to produce non-trivial (closed) invariant subspaces of (bounded
linear) operators. Also a topological tool is used which is new in
the search of invariant subspaces: the extraction of continuous
selections of lower semicontinuous set valued functions. The advantage
of this method over previously known methods is that if an operator
acts on a reflexive Banach space then it has a non-trivial invariant
subspace if and only if there exist compatible sequences (their
definition refers to a fixed operator). Using compatible sequences
a result of Aronszajn-Smith is proved for reflexive Banach spaces.
Also it is shown that if $X$ be a separable reflexive Banach space,
$T \in {\mathcal L} (X)$, and $A$ is any closed ball of $X$, then
there exists $v \in A$ such that either $Tv=0$, or
$\overline{\text{Span}}\, \text{Orb}_T (Tv)$ is a non-trivial
invariant subspace of $T$, or there exists a continuous function
$f:A \to A$ where $A$ is endowed with the weak topology, such that
$f(x) \in \overline{\text{Span}}\, \{ T^k x : k \in {\mathbb N} \}
$ for all $x \in A$ and $f(v)=v$.
Archive classification: Functional Analysis
Mathematics Subject Classification: 47A15
The source file(s), ISP.tex: 60926 bytes, is(are) stored in gzipped
form as 0506284.gz with size 17kb. The corresponding postcript file
has gzipped size 78kb.
Submitted from: giorgis at math.sc.edu
The paper may be downloaded from the archive by web browser from
URL
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From alspach at www.math.okstate.edu Tue Jun 21 07:48:05 2005
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Date: Tue, 21 Jun 2005 07:48:05 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200506211248.j5LCm5Yh083993 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by U. Bader, A. Furman, T. Gelander, and N. Monod
Status: R
This is an announcement for the paper "Property (T) and rigidity
for actions on Banach spaces" by U. Bader, A. Furman, T. Gelander,
and N. Monod.
Abstract: We study property (T) and the fixed point property for
actions on $L^p$ and other Banach spaces. We show that property (T)
holds when $L^2$ is replaced by $L^p$ (and even a subspace/quotient
of $L^p$), and that in fact it is independent of $1\leq p<\infty$.
We show that the fixed point property for $L^p$ follows from property
(T) when $1<p< 2+\e$. For simple Lie groups and their lattices, we
prove that the fixed point property for $L^p$ holds for any $1<
p<\infty$ if and only if the rank is at least two. Finally, we
obtain a superrigidity result for actions of irreducible lattices
in products of general groups on superreflexive Banach spaces.
Archive classification: Group Theory; Functional Analysis
The source file(s), ftlp14.tex: 137939 bytes, is(are) stored in
gzipped form as 0506361.gz with size 43kb. The corresponding postcript
file has gzipped size 152kb.
Submitted from: monod at math.uchicago.edu
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.GR/0506361
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http://arXiv.org/abs/math.GR/0506361
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From alspach at www.math.okstate.edu Mon Jul 4 10:08:53 2005
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Date: Mon, 4 Jul 2005 10:08:53 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200507041508.j64F8rmA094191 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Olivier Guedon and Mark Rudelson
Status: R
This is an announcement for the paper "L_p moments of random vectors
via majorizing measures" by Olivier Guedon and Mark Rudelson.
Abstract: For a random vector X in R^n, we obtain bounds on the
size of a sample, for which the empirical p-th moments of linear
functionals are close to the exact ones uniformly on a given convex
body K. We prove an estimate for a general random vector and apply
it to several problems arising in geometric functional analysis.
In particular, we find a short Lewis type decomposition for any
finite dimensional subspace of L_p and study in detail the case of
an isotropic log-concave random vector. We also prove a concentration
estimate for the empirical moments. The main ingredient of the proof
is the construction of an appropriate majorizing measure to bound
a certain Gaussian process.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B09, 52A21
Remarks: 33 pages
The source file(s), gr05-06-16.tex: 72987 bytes, is(are) stored in
gzipped form as 0507023.gz with size 21kb. The corresponding postcript
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Submitted from: rudelson at math.missouri.edu
The paper may be downloaded from the archive by web browser from
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From alspach at www.math.okstate.edu Mon Jul 4 10:09:35 2005
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Date: Mon, 4 Jul 2005 10:09:35 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200507041509.j64F9Zmb094222 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Mark Rudelson
Status: R
This is an announcement for the paper "Invertibility of random
matrices: norm of the inverse" by Mark Rudelson.
Abstract: Let A be an n by n matrix, whose entries are independent
copies of a centered random variable satisfying the subgaussian
tail estimate. We prove that the operator norm of A^{-1} does not
exceed Cn^{3/2} with probability close to 1.
Archive classification: Functional Analysis
Mathematics Subject Classification: 15A52, 46B09
Remarks: 25 pages
The source file(s), square-matrix.tex: 58844 bytes, is(are) stored
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postcript file has gzipped size 94kb.
Submitted from: rudelson at math.missouri.edu
The paper may be downloaded from the archive by web browser from
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From alspach at www.math.okstate.edu Tue Jul 19 08:31:47 2005
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Date: Tue, 19 Jul 2005 08:31:47 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200507191331.j6JDVlw6020205 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Hermann Pfitzner
Status: R
This is an announcement for the paper "A separable L-embedded Banach
space has property (X) and is therefore the unique predual of its
dual" by Hermann Pfitzner.
Abstract: In this note the following is proved. Separable L-embedded
spaces - that is separable Banach spaces which are complemented in
their biduals such that the norm between the two complementary
subspaces is additive - have property (X) which, by a result of
Godefroy and Talagrand, entails uniqueness of the space as a predual.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B04, 46B03, 46B20
The source file(s), Property_X.tex: 22448 bytes, is(are) stored in
gzipped form as 0507354.gz with size 8kb. The corresponding postcript
file has gzipped size 41kb.
Submitted from: Hermann.Pfitzner at univ-orleans.fr
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0507354
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From banach-bounces at math.okstate.edu Wed Jul 20 18:59:46 2005
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Date: Wed, 20 Jul 2005 18:58:44 -0500
From: Dale Alspach <alspach at math.okstate.edu>
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Subject: [Banach] Pictures of Haskell Rosenthal
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Status: R
Haskell Rosenthal retired from The University of Texas this past fall after a
long and distinguished career. Haskell's wife, Gayle Rosenthal, would like to
receive copies of any photos or e-photos or discs, anything with photos of
Haskell, lecturing, hiking, dancing, drinking, or anything else, including
photos of friends or places he's known or been to. She is preparing a video
montage to be shown during Haskellfest at Texas A&M University, August 4-5,
2005.
e-Photos should be sent to:
Gayle Rosenthal <gayle-rosenthal at austin.rr.com>
Hard copies of photos should be sent to:
Gayle Rosenthal
311 Nixon Drive
Austin TX 78746
_______________________________________________
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From alspach at www.math.okstate.edu Tue Jul 26 09:50:08 2005
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Date: Tue, 26 Jul 2005 09:50:08 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200507261450.j6QEo8tS080774 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by E. Odell and Th. Schlumprecht
Status: R
This is an announcement for the paper "A universal reflexive space
for the class of uniformly convex Banach spaces" by E. Odell and
Th. Schlumprecht.
Abstract: We show that there exists a separable reflexive Banach
space into which every separable uniformly convex Banach space
isomorphically embeds. This solves a problem of J.~Bourgain. We
also give intrinsic characterizations of separable reflexive Banach
spaces which embed into a reflexive space with a block $q$-Hilbertian
and/or a block $p$-Besselian finite dimensional decomposition.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B03; secondary 46B20
Remarks: 13 pages, amslatex
The source file(s), os-universal2-archive.tex: 45823 bytes, is(are)
stored in gzipped form as 0507509.gz with size 14kb. The corresponding
postcript file has gzipped size 78kb.
Submitted from: combs at mail.ma.utexas.edu
The paper may be downloaded from the archive by web browser from
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From alspach at www.math.okstate.edu Mon Aug 8 10:16:56 2005
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Date: Mon, 8 Aug 2005 10:16:56 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200508081516.j78FGuIb035805 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Marc A. Rieffel
Status: R
This is an announcement for the paper "Lipschitz extension constants
equal projection constants" by Marc A. Rieffel.
Abstract: For a finite-dimensional Banach space $V$ we define its
Lipschitz extension constant, $\cL\cE(V)$, to be the smallest
constant $c$ such that for every compact metric space $(Z,\rho)$,
every $X \subset Z$, and every $f: X \to V$, there is an extension,
$g$, of $f$ to $Z$ such that $L(g) \le cL(f)$, where $L$ denotes
the Lipschitz constant. Our main theorem is that $\cL\cE(V) =
\cP\cC(V)$ where $\cP\cC(V)$ is the well-known projection constant
of $V$. We obtain some consequences, especially when $V = M_n(\bC)$.
We also discuss what happens if we also require that $\|g\|_{\infty}
= \|f\|_{\infty}$.
Archive classification: Functional Analysis; Metric Geometry
Mathematics Subject Classification: 46B20; 26A16
Remarks: 12 pages. Intended for the proceedings of GPOTS05
The source file(s), liparc.tex: 35141 bytes, is(are) stored in
gzipped form as 0508097.gz with size 12kb. The corresponding postcript
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From alspach at www.math.okstate.edu Thu Aug 18 12:07:53 2005
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Date: Thu, 18 Aug 2005 12:07:53 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200508181707.j7IH7rlf070712 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by A K Mirmostafaee
Status: RO
This is an announcement for the paper "A note on convex renorming
and fragmentability" by A K Mirmostafaee.
Abstract: Using the game approach to fragmentability, we give new
and simpler proofs of the following known results: (a)~If the Banach
space admits an equivalent Kadec norm, then its weak topology is
fragmented by a metric which is stronger than the norm topology.
(b)~If the Banach space admits an equivalent rotund norm, then its
weak topology is fragmented by a metric. (c)~If the Banach space
is weakly locally uniformly rotund, then its weak topology is
fragmented by a metric which is stronger than the norm topology.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B20, 54E99, 54H05
Citation: Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 2,
May 2005,
The paper may be downloaded from the archive by web browser from
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http://front.math.ucdavis.edu/math.FA/0508311
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From alspach at www.math.okstate.edu Fri Aug 26 12:24:41 2005
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Date: Fri, 26 Aug 2005 12:24:41 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200508261724.j7QHOfSl024777 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Javier Parcet
Status: R
This is an announcement for the paper "Weak type estimates associated
to Burkholder's martingale inequality" by Javier Parcet.
Abstract: Given a probability space $(\Omega, \mathsf{A}, \mu)$,
let $\mathsf{A}_1, \mathsf{A}_2, \ldots$ be a filtration of
$\sigma$-subalgebras of $\mathsf{A}$ and let $\mathsf{E}_1,
\mathsf{E}_2, \ldots$ denote the corresponding family of conditional
expectations. Given a martingale $f = (f_1, f_2, \ldots)$ adapted
to this filtration and bounded in $L_p(\Omega)$ for some $2 \le p
< \infty$, Burkholder's inequality claims that $$\|f\|_{L_p(\Omega)}
\sim_{\mathrm{c}_p} \Big\| \Big( \sum_{k=1}^\infty
\mathsf{E}_{k-1}(|df_k|^2) \Big)^{1/2} \Big\|_{L_{p}(\Omega)} +
\Big( \sum_{k=1}^\infty \|df_k\|_p^p \Big)^{1/p}.$$ Motivated by
quantum probability, Junge and Xu recently extended this result to
the range $1 < p < 2$. In this paper we study Burkholder's inequality
for $p=1$, for which the techniques (as we shall explain) must be
different. Quite surprisingly, we obtain two non-equivalent estimates
which play the role of the weak type $(1,1)$ analog of Burkholder's
inequality. As application, we obtain new properties of Davis
decomposition for martingales.
Archive classification: Probability; Functional Analysis
Mathematics Subject Classification: 42B25; 60G46; 60G50
Remarks: 19 pages
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Submitted from: javier.parcet at uam.es
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From banach-bounces at math.okstate.edu Fri Aug 26 12:39:09 2005
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From: Dale Alspach <alspach at math.okstate.edu>
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Subject: [Banach] Abstract of a paper by Gilles Pisier
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Status: R
This is an announcement for the paper "Simultaneous similarity,
bounded generation and amenability" by Gilles Pisier.
Abstract: We prove that a discrete group $G$ is amenable iff it is
strongly unitarizable in the following sense: every unitarizable
representation $\pi$ on $G$ can be unitarized by an invertible
chosen in the von Neumann algebra generated by the range of $\pi$.
Analogously a $C^*$-algebra $A$ is nuclear iff any bounded homomorphism
$u:\ A\to B(H)$ is strongly similar to a $*$-homomorphism in the
sense that there is an invertible operator $\xi$ in the von Neumann
algebra generated by the range of $u$ such that $a\to \xi u(a)
\xi^{-1}$ is a $*$-homomorphism. An analogous characterization holds
in terms of derivations. We apply this to answer several questions
left open in our previous work concerning the length $\ell(A,B)$
of the maximal tensor product $A\otimes_{\max} B$ of two unital
$C^*$-algebras, when we consider its generation by the subalgebras
$A\otimes 1$ and $1\otimes B$. We show that if
$\ell(A,B)<\infty$ either for $B=B(\ell_2)$ or when $B$ is the
$C^*$-algebra
(either full or reduced) of a non Abelian free group, then $A$ must
be nuclear. We also show that $\ell(A,B)\le d$ iff the canonical
quotient map from the unital free product $A\ast B$ onto $A\otimes_{\max}
B$ remains a complete quotient map when restricted to the closed
span of the words of length $\le d$.
Archive classification: Operator Algebras; Functional Analysis
Mathematics Subject Classification: Primary 46 L06. Secondary: 46L07,
46L57 Primary 46 L06. Secondary:
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.OA/0508223
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From alspach at www.math.okstate.edu Fri Aug 26 12:27:21 2005
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200508261727.j7QHRLxa024822 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Anna Maria Pelczar
Status: R
This is an announcement for the paper "Stabilization of Tsirelson-type
norms on $\ell_p$ spaces" by Anna Maria Pelczar.
Abstract: We consider classical Tsirelson-type norms of $T[A_r,\theta]$
and their modified versions on $\ell_p$ spaces. We show that for
any $1<p<\infty$ there is a constant $\lambda_p$ such that considered
Tsirelson-type norms do not $\lambda_p$-distort any of subspaces
of $\ell_p$.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B03
Remarks: 10 pages
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Submitted from: anna.pelczar at im.uj.edu.pl
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From banach-bounces at math.okstate.edu Fri Aug 26 12:42:46 2005
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Subject: [Banach] Abstract of a paper by A K Mirmostafaee
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Status: R
This is an announcement for the paper "A note on convex renorming
and fragmentability" by A K Mirmostafaee.
Abstract: Using the game approach to fragmentability, we give new
and simpler proofs of the following known results: (a)~If the Banach
space admits an equivalent Kadec norm, then its weak topology is
fragmented by a metric which is stronger than the norm topology.
(b)~If the Banach space admits an equivalent rotund norm, then its
weak topology is fragmented by a metric. (c)~If the Banach space
is weakly locally uniformly rotund, then its weak topology is
fragmented by a metric which is stronger than the norm topology.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B20, 54E99, 54H05
Citation: Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 2,
May 2005,
The paper may be downloaded from the archive by web browser from
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http://front.math.ucdavis.edu/math.FA/0508311
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_______________________________________________
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From alspach at www.math.okstate.edu Tue Aug 30 07:43:39 2005
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Message-Id: <200508301243.j7UChcIo097667 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Mukul S. Patel
Status: R
This is an announcement for the paper "Noncommmutative Gelfand
duality for not necessarily unital $C^*$-algebras, Jordan canonical
form, and the existence of invariant subspaces" by Mukul S. Patel.
Abstract: Gelfand-Naimark duality (Commutative $C^*$-algebras
$\equiv$ Locally compact Hausdorff spaces) is extended to
\begin{center}$C^*$-algebras $\equiv$ Quotient maps on locally
compact Hausdorff spaces.\end{center} Using this duality, we give
for an \emph{arbitrary} bounded operator on a complex Hilbert space
of several dimensions, a functional calculus and the existence
theorem for nontrivial invariant subspace.
Archive classification: Functional Analysis; Operator Algebras
Mathematics Subject Classification: 46L05; 47A13; 47A13; 43A40;
22B05
Remarks: Under consideration for publication by Electronic Reasearch
The paper may be downloaded from the archive by web browser from
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From alspach at www.math.okstate.edu Thu Sep 1 06:36:28 2005
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Date: Thu, 1 Sep 2005 06:36:28 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200509011136.j81BaSeL020164 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by S. J. Dilworth, E. Odell and B. Sari
Status: R
This is an announcement for the paper "Lattice structures and
spreading models" by S. J. Dilworth, E. Odell and B. Sari.
Abstract: We consider problems concerning the partial order structure
of the set of spreading models of Banach spaces. We construct
examples of spaces showing that the possible structure of these
sets include certain classes of finite semi-lattices and countable
lattices, and all finite lattices.
Archive classification: Functional Analysis
The source file(s), dos.tex: 60915 bytes, is(are) stored in gzipped
form as 0508650.gz with size 19kb. The corresponding postcript file
has gzipped size 88kb.
Submitted from: bunyamin at unt.edu
The paper may be downloaded from the archive by web browser from
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From alspach at www.math.okstate.edu Tue Sep 13 11:37:11 2005
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Date: Tue, 13 Sep 2005 11:37:11 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200509131637.j8DGbBvj023201 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by N. Brodskiy and D. Sonkin
Status: R
This is an announcement for the paper "Compression of uniform
embeddings into Hilbert space" by N. Brodskiy and D. Sonkin.
Abstract: If one tries to embed a metric space uniformly in Hilbert
space, how close to quasi-isometric could the embedding be? We
answer this question for finite dimensional CAT(0) cube complexes
and for hyperbolic groups. In particular, we show that the Hilbert
space compression of any hyperbolic group is 1.
Archive classification: Group Theory; Functional Analysis; Geometric
Topology
Mathematics Subject Classification: 20F69; 20F65; 46C05
Remarks: 10 pages
The source file(s), Uniform_Embeddings.tex: 27243 bytes, is(are)
stored in gzipped form as 0509108.gz with size 9kb. The corresponding
postcript file has gzipped size 50kb.
Submitted from: brodskiy at math.utk.edu
The paper may be downloaded from the archive by web browser from
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From alspach at www.math.okstate.edu Tue Sep 13 11:37:37 2005
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Date: Tue, 13 Sep 2005 11:37:37 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200509131637.j8DGbbJD023232 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Narcisse Randrianantoanina
Status: R
This is an announcement for the paper "Conditioned square functions
for non-commutative martingales" by Narcisse Randrianantoanina.
Abstract: We prove a weak-type (1,1) inequality involving conditioned
square functions of martingales in non-commutative $L^p$-spaces
associated with finite von Neumann algebras. As application, we
determine the optimal orders for the best constants in the
non-commutative Burkholder/Rosenthal inequalities from Ann. Proba.
31 (2003), 948-995. We also discuss BMO-norms of sums of non-commuting
order independent operators.
Archive classification: Functional Analysis; Probability
Mathematics Subject Classification: 46L53; 60G42
Remarks: 38 pages
The source file(s), condsquaref.tex: 107932 bytes, is(are) stored
in gzipped form as 0509226.gz with size 31kb. The corresponding
postcript file has gzipped size 136kb.
Submitted from: randrin at muohio.edu
The paper may be downloaded from the archive by web browser from
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From alspach at www.math.okstate.edu Fri Sep 16 21:57:45 2005
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Date: Fri, 16 Sep 2005 21:57:45 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200509170257.j8H2vjQs000379 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jan van Neerven
Status: R
This is an announcement for the paper "Separated sequences in
uniformly convex Banach spaces" by Jan van Neerven.
Abstract: We prove that the unit sphere of every infinite-dimensional
uniformly convex Banach space with modulus of convexity $\delta$
contains a $(1+\frac12\delta(\frac23))$-separated sequence.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B20
Citation: Colloq. Math. 102 (2005), 147-153
Remarks: 5 pages
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postcript file has gzipped size 33kb.
Submitted from: J.vanNeerven at math.tudelft.nl
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URL
http://front.math.ucdavis.edu/math.FA/0509344
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Date: Fri, 16 Sep 2005 21:56:49 CDT
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
From: Dale Alspach <alspach at www.math.okstate.edu>
Subject: [Banach] Abstract of a paper by Gilles Pisier
This is an announcement for the paper "Remarks on $B(H)\otimes
B(H)$" by Gilles Pisier.
Abstract: We review the existing proofs that the min and max norms
are different on $B(H)\otimes B(H)$ and give a shortcut avoiding
the consideration of non-separable families of operator spaces.
Archive classification: Operator Algebras; Functional Analysis
Mathematics Subject Classification: 46L05, 46M05, 47D15
The source file(s), remarks.BB.tex: 17702 bytes, is(are) stored in
gzipped form as 0509297.gz with size 7kb. The corresponding postcript
file has gzipped size 43kb.
Submitted from: gip at ccr.jussieu.fr
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From alspach at www.math.okstate.edu Sat Sep 17 08:02:59 2005
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Date: Sat, 17 Sep 2005 08:02:58 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200509171302.j8HD2wAp007469 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Yevgen Ivakhno, Vladimir Kadets and Dirk Werner
Status: R
This is an announcement for the paper "The Daugavet property for
spaces of Lipschitz functions" by Yevgen Ivakhno, Vladimir Kadets
and Dirk Werner.
Abstract: For a compact metric space $K$ the space $\Lip(K)$ has
the Daugavet property if and only if the norm of every $f \in
\Lip(K)$ is attained locally. If $K$ is a subset of an $L_p$-space,
$1<p<\infty$, this is equivalent to the convexity of~$K$.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B04; 46B25; 54E45
The source file(s), daugalip.tex: 46665 bytes, is(are) stored in
gzipped form as 0509373.gz with size 15kb. The corresponding postcript
file has gzipped size 75kb.
Submitted from: werner at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from
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From alspach at www.math.okstate.edu Sat Sep 17 08:03:55 2005
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Date: Sat, 17 Sep 2005 08:03:55 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200509171303.j8HD3t60007501 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Konstantin Boyko, Vladimir Kadets, Miguel Martin, and Dirk Werner
Status: R
This is an announcement for the paper "Numerical index and duality"
by Konstantin Boyko, Vladimir Kadets, Miguel Martin, and Dirk Werner.
Abstract: We present an example of a Banach space whose numerical
index is strictly greater than the numerical index of its dual,
giving a negative answer to a question which has been latent since
the beginning of the seventies. We also show a particular case in
which the numerical index of the space and the one of its dual
coincide.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B20; 47A12; 46B22; 46E15
The source file(s), miguelvovakostya.tex: 34653 bytes, is(are)
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postcript file has gzipped size 63kb.
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From alspach at www.math.okstate.edu Tue Sep 20 07:38:07 2005
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Date: Tue, 20 Sep 2005 07:38:07 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200509201238.j8KCc7k8056320 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann, and V.G. Troitsky
Status: R
This is an announcement for the paper "On norm closed ideals in
L(\ell_p\oplus\ell_q)" by B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann,
and V.G. Troitsky.
Abstract: It is well known that the only proper non-trivial norm-closed
ideal in the algebra L(X) for X=\ell_p (1 \le p < \infty) or X=c_0
is the ideal of compact operators. The next natural question is to
describe all closed ideals of L(\ell_p\oplus\ell_q) for 1 \le p,q
< \infty, p \neq q, or, equivalently, the closed ideals in
L(\ell_p,\ell_q) for p < q. This paper shows that for 1 < p < 2 <
q < \infty there are at least four distinct proper closed ideals
in L(\ell_p,\ell_q), including one that has not been studied before.
The proofs use various methods from Banach space theory.
Archive classification: Functional Analysis; Operator Algebras
Mathematics Subject Classification: 47L20; 47B10; 47B37
Remarks: 24 pages
Submitted from: vtroitsky at math.ualberta.ca
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0509414
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From alspach at www.math.okstate.edu Thu Sep 22 13:32:41 2005
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Date: Thu, 22 Sep 2005 13:32:41 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200509221832.j8MIWfZ5081377 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by A.Hajji
Status: R
This is an announcement for the paper "Forme equivalente \`a la
condition $\Delta_2 $ et certains r\'esultats de s\'eparations
dans les espaces modulaires" by A.Hajji.
Abstract: In this paper, we present an equivalent form of the
$\Delta_2 $-condition which allow us to redefine the topological
vector space structure of a modular spaces using the \\ filter base.
We show also the characterization of closed subsets (in the sens
of this topology ) of a modular spaces which permit us to establish
some separation results in modular spaces
Archive classification: Functional Analysis
Remarks: 11p,pas de figure
The source file(s), E12.tex: 25102 bytes, is(are) stored in gzipped
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has gzipped size 41kb.
Submitted from: lphe at fsr.ac.ma
The paper may be downloaded from the archive by web browser from
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From alspach at www.math.okstate.edu Tue Oct 4 06:49:06 2005
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Date: Tue, 4 Oct 2005 06:49:05 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200510041149.j94Bn5jF066692 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Peter G. Casazza, Matt Fickus, Janet C. Tremain, and Eric Weber
Status: R
This is an announcement for the paper "The Kadison-Singer problem
in mathematics and engineering" by Peter G. Casazza, Matt Fickus,
Janet C. Tremain, and Eric Weber.
Abstract: We will show that the famous, intractible 1959 Kadison-Singer
problem in $C^{*}$-algebras is equivalent to fundamental unsolved
problems in a dozen areas of research in pure mathematics, applied
mathematics and Engineering. This gives all these areas common
ground on which to interact as well as explaining why each of these
areas has volumes of literature on their respective problems without
a satisfactory resolution. In each of these areas we will reduce
the problem to the minimum which needs to be proved to solve their
version of Kadison-Singer. In some areas we will prove what we
believe will be the strongest results ever available in the case
that Kadison-Singer fails. Finally, we will give some directions
for constructing a counter-example to Kadison-Singer.
Archive classification: Functional Analysis
Mathematics Subject Classification: 42C15; 46B03; 46C05; 47A05;
46L05; 46L10
The source file(s), KSSubmit.tex: 163819 bytes, is(are) stored in
gzipped form as 0510024.gz with size 46kb. The corresponding postcript
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Submitted from: pete at math.missouri.edu
The paper may be downloaded from the archive by web browser from
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From: Dale Alspach <alspach at math.okstate.edu>
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Subject: [Banach] Conference on Banach spaces and their Applications in
Analysis
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Status: R
Second Announcement for the conference
``Banach spaces and their applications in Analysis'',
in honor of Nigel Kalton's 60th birthday,
to be held May 22-27, 2006 at Miami University in
Oxford, Ohio.
We would like to announce that the website for the conference
has been updated and now includes information about registration
fees and deadlines for submitting abstracts and payments.
At the conference we will emphasize the following themes:
- -- Nonlinear theory (Lipschitz classifications of Banach and
metric spaces and related topics),
- -- Isomorphic theory of Banach spaces including connections with
combinatorics and set theory,
- -- Algebraic and homological methods in Banach spaces,
- -- Approximation theory and algorithms in Banach spaces
(greedy algorithms, interpolation etc.),
- -- Functional calculus and applications to Partial Differential
Equations.
The following people have agreed to be principal speakers at the conference:
Yuri Brudnyi (Technion - Israel Institute of Technology, Israel)
Jesus M. F. Castillo (University of Extremadura, Spain)
Marianna Csornyei (University College, London, UK)
Stephen Dilworth (University of South Carolina)
Gilles Godefroy (Universitè Paris VI, France)
William B. Johnson (Texas A&M University)
Joram Lindenstrauss (Hebrew University, Israel)
Assaf Naor (Microsoft Research)
Edward Odell (University of Texas)
Aleksander Pelczynski (Polish Academy of Sciences, Poland)
David Preiss (University College, London, UK)
Gideon Schechtman (Weizmann Institute of Science, Israel)
Thomas Schlumprecht (Texas A&M University)
Vladimir Temlyakov (University of South Carolina)
Nicole Tomczak-Jaegermann (University of Alberta, Canada)
Roman Vershynin (University of California - Davis)
Lutz Weis (Universitat Karlsruhe, Germany)
Przemyslaw Wojtaszczyk (Warsaw University, Poland)
More information about the conference, its
location, registration fees, deadlines,
accommodations and a printable poster are available at the website:
http://www.users.muohio.edu/randrib/bsaa2006.html
Please direct any questions to either of the organizers at randrib at muohio.edu
or randrin at muohio.edu
Sincerely yours,
Beata Randrianantoanina
Narcisse Randrianantoanina.
_______________________________________________
Banach mailing list
Banach at math.okstate.edu
http://mail.math.okstate.edu/mailman/listinfo/banach
From alspach at www.math.okstate.edu Thu Oct 20 13:10:00 2005
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Date: Thu, 20 Oct 2005 13:10:00 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200510201810.j9KIA0Zk033210 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Matthew Neal and Bernard Russo
Status: R
This is an announcement for the paper "Classification of contractively
complemented Hilbertian operator spaces" by Matthew Neal and Bernard
Russo.
Abstract: We construct some separable infinite dimensional homogeneous
Hilbertian operator spaces which generalize the row and column
spaces R and C. We show that separable infinite-dimensional Hilbertian
JC*-triples are completely isometric to an element of the set of
(infinite) intersections of these spaces. This set includes the
operator spaces R, C, their intersection, and the space spanned by
creation operators on the full anti-symmetric Fock space. In fact,
we show that these new spaces are completely isometric to the space
of creation (resp. annihilation) operators on the anti-symmetric
tensors of the Hilbert space. Together with the finite-dimensional
case studied in our previous paper, this gives a full operator space
classification of all rank-one JC*-triples in terms of creation and
annihilation operator spaces.
We use the above to show that all contractive projections on a
C*-algebra A
with infinite dimensional Hilbertian range are ``expansions'' (which
we define precisely) of normal contractive projections from the
second dual of A onto a Hilbertian space which is completely isometric
to one of the four spaces mentioned above. This generalizes the
well known result, first proved for B(H) by Robertson, that all
Hilbertian operator spaces that are completely contractively
complemented in a C*-algebra are completely isometric to R or C.
We also compute various completely bounded Banach-Mazur distances
between these spaces.
Archive classification: Operator Algebras; Functional Analysis
Mathematics Subject Classification: 46L07
Remarks: 24 pages, submitted
The source file(s), fock0827.tex: 87070 bytes, is(are) stored in
gzipped form as 0510323.gz with size 27kb. The corresponding postcript
file has gzipped size 117kb.
Submitted from: brusso at math.uci.edu
The paper may be downloaded from the archive by web browser from
URL
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From alspach at www.math.okstate.edu Thu Oct 20 13:10:58 2005
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Date: Thu, 20 Oct 2005 13:10:58 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200510201810.j9KIAwpM033254 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jordi Lopez Abad and S. Todorcevic
Status: R
This is an announcement for the paper "Pre-compact families of
finite sets of integers and weakly null sequences in Banach spaces"
by Jordi Lopez Abad and S. Todorcevic.
Abstract: We provide a somewhat general framework for studying
weakly null sequences in Banach spaces using Ramsey theory of
families of finite subsets of integers
Archive classification: Functional Analysis; Logic
Mathematics Subject Classification: MSC: 05d10, 46b20
The source file(s), lop-tod.tex: 145237 bytes, is(are) stored in
gzipped form as 0510407.gz with size 41kb. The corresponding postcript
file has gzipped size 136kb.
Submitted from: abad at logique.jussieu.fr
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0510407
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http://arXiv.org/abs/math.FA/0510407
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From alspach at www.math.okstate.edu Thu Oct 20 13:11:59 2005
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Date: Thu, 20 Oct 2005 13:11:59 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200510201811.j9KIBxTS033298 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jordi Lopez Abad and Antonis Manoussakis
Status: R
This is an announcement for the paper "A classification of Tsirelson
type spaces" by Jordi Lopez Abad and Antonis Manoussakis.
Abstract: We give a complete classification of mixed Tsirelson
spaces T[( F\_i, theta\_i)\_{i=1}^r ] for finitely many pairs of
given compact and hereditary families F\_i of finite sets of integers
and 0<theta\_i<1 in terms of the Cantor-Bendixson indexes of the
families F\_i, and theta\_i (0< i < r+1). We prove that there are
unique countable ordinal alpha and 0<theta<1 such that every block
sequence of T[( F\_i, theta\_i)\_{i=1}^r ] has a subsequence
equivalent to a subsequence of the natural basis of the T(
S\_{omega^alpha},theta ). Finally, we give a complete criterion of
comparison in between two of these mixed Tsirelson spaces.
Archive classification: Functional Analysis; Logic
Mathematics Subject Classification: MSC 46b20, 05d10
The source file(s), lop-man.tex: 131413 bytes, is(are) stored in
gzipped form as 0510410.gz with size 37kb. The corresponding postcript
file has gzipped size 150kb.
Submitted from: abad at logique.jussieu.fr
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0510410
or
http://arXiv.org/abs/math.FA/0510410
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From alspach at www.math.okstate.edu Thu Oct 27 08:33:24 2005
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Date: Thu, 27 Oct 2005 08:33:23 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200510271333.j9RDXNhc026298 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Ulrich Kohlenbach and Laurentiu Leustean
Status: R
This is an announcement for the paper "The approximate fixed point
property in product spaces" by Ulrich Kohlenbach and Laurentiu
Leustean.
Abstract: In this paper we generalize to unbounded convex subsets
C of hyperbolic spaces results obtained by W.A. Kirk and R. Espinola
on approximate fixed points of nonexpansive mappings in product
spaces $(C\times M)_\infty$, where M is a metric space and C is a
nonempty, convex, closed and bounded subset of a normed or a
CAT(0)-space. We extend the results further, to families $(C_u)_{u\in
M}$ of unbounded convex subsets of a hyperbolic space. The key
ingredient in obtaining these generalizations is a uniform quantitative
version of a theorem due to Borwein, Reich and Shafrir, obtained
by the authors in a previous paper using techniques from mathematical
logic. Inspired by that, we introduce in the last section the notion
of uniform approximate fixed point property for sets C and classes
of self-mappings of C. The paper ends with an open problem.
Archive classification: Functional Analysis; Logic
Mathematics Subject Classification: 47H10, 47H09 (Primary) 03F10
(Secondary)
Remarks: 15 pages
The source file(s), AFPP.tex: 38299 bytes, is(are) stored in gzipped
form as 0510563.gz with size 10kb. The corresponding postcript file
has gzipped size 62kb.
Submitted from: leustean at mathematik.tu-darmstadt.de
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0510563
or
http://arXiv.org/abs/math.FA/0510563
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uget 0510563
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From alspach at www.math.okstate.edu Thu Oct 27 08:34:11 2005
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Date: Thu, 27 Oct 2005 08:34:11 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200510271334.j9RDYBYm026329 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Subhash Khot and Assaf Naor
Status: R
This is an announcement for the paper "Nonembeddability theorems
via Fourier analysis" by Subhash Khot and Assaf Naor.
Abstract: Various new nonembeddability results (mainly into $L_1$)
are proved via Fourier analysis. In particular, it is shown that
the Edit Distance on $\{0,1\}^d$ has $L_1$ distortion $(\log
d)^{\frac12-o(1)}$. We also give new lower bounds on the $L_1$
distortion of flat tori, quotients of the discrete hypercube under
group actions, and the transportation cost (Earthmover) metric.
Archive classification: Functional Analysis; Metric Geometry
Mathematics Subject Classification: 46B20; 68U05
Remarks: With an appendix on quantitative estimates in Bourgain's
noise
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0510547
or
http://arXiv.org/abs/math.FA/0510547
or by email in unzipped form by transmitting an empty message with
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uget 0510547
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From alspach at www.math.okstate.edu Fri Oct 28 14:59:48 2005
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Date: Fri, 28 Oct 2005 14:59:48 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200510281959.j9SJxmEF061334 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by S. J. Dilworth, E. Odell, Th. Schlumprecht and A. Zsak
Status: R
This is an announcement for the paper "Partial Unconditionality"
by S. J. Dilworth, E. Odell, Th. Schlumprecht and A. Zsak.
Abstract: J. Elton proved that every normalized weakly null sequence
in a Banach space admits a subsequence that is nearly unconditional
which is a weak form of unconditionality. The notion of
near-unconditionality is quantified by a constant $K(\delta)$
depending on a parameter $\delta \in (0,1]$. It is unknown if
$\sup_{\delta>0} K(\delta) < \infty$. This problem turns out to be
closely related to the question whether every infinite-dimensional
Banach space contains a quasi-greedy basic sequence. The notion of
a quasi-greedy basic sequence was introduced recently by S. V.
Konyagin and V. N. Temlyakov. We present an extension of Elton's
result which includes Schreier unconditionality. The proof involves
a basic framework which we show can be also employed to prove other
partial unconditionality results including that of convex
unconditionality due to Argyros, Mercourakis and Tsarpalias. Various
constants of partial unconditionality are defined and we investigate
the relationships between them. We also explore the combinatorial
problem underlying the $\sup_{\delta>0} K(\delta) < \infty$ problem
and show that $\sup_{\delta>0} K(\delta) > 5/4$.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B15
Remarks: 50 pages
The source file(s), partial_unconditionality.tex: 175575 bytes,
is(are) stored in gzipped form as 0510609.gz with size 46kb. The
corresponding postcript file has gzipped size 196kb.
Submitted from: a.zsak at dpmms.cam.ac.uk
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0510609
or
http://arXiv.org/abs/math.FA/0510609
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uget 0510609
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From alspach at www.math.okstate.edu Fri Oct 28 15:01:10 2005
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Date: Fri, 28 Oct 2005 15:01:09 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200510282001.j9SK19Kh061395 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by D. Azagra and M. Jimenez-Sevilla
Status: R
This is an announcement for the paper "Approximation by smooth
functions with no critical points on separable Banach spaces" by
D. Azagra and M. Jimenez-Sevilla.
Abstract: We characterize the class of separable Banach spaces $X$
such that for every continuous function $f:X\to\mathbb{R}$ and for
every continuous function $\varepsilon:X\to\mathbb(0,+\infty)$ there
exists a $C^1$ smooth function $g:X\to\mathbb{R}$ for which
$|f(x)-g(x)|\leq\varepsilon(x)$ and $g'(x)\neq 0$ for all $x\in X$
(that is, $g$ has no critical points), as those Banach spaces $X$
with separable dual $X^*$. We also state sufficient conditions on
a separable Banach space so that the function $g$ can be taken to
be of class $C^p$, for $p=1,2,..., +\infty$. In particular, we
obtain the optimal order of smoothness of the approximating functions
with no critical points on the classical spaces $\ell_p(\mathbb{N})$
and $L_p(\mathbb{R}^n)$. Some important consequences of the above
results are (1) the existence of {\em a non-linear Hahn-Banach
theorem} and (2) the smooth approximation of closed sets, on the
classes of spaces considered above.
Archive classification: Functional Analysis; Differential Geometry
Mathematics Subject Classification: 46B20; 46T30; 58E05; 58C25
Remarks: 34 pages
The source file(s), critical270905.tex: 127379 bytes,
separable2argument.eps: 46690 bytes, separable3argument.eps: 48762
bytes, separable3bargument.eps: 48459 bytes, sinbase2.eps: 47562
bytes, is(are) stored in gzipped form as 0510603.tar.gz with size
90kb. The corresponding postcript file has gzipped size 220kb.
Submitted from: daniel_azagra at mat.ucm.es
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0510603
or
http://arXiv.org/abs/math.FA/0510603
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From alspach at www.math.okstate.edu Tue Nov 1 10:59:02 2005
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Date: Tue, 1 Nov 2005 10:59:02 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200511011659.jA1Gx2wV017175 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jakub Duda
Status: R
This is an announcement for the paper "Cone monotone mappings:
continuity and differentiability" by Jakub Duda.
Abstract: We generalize some results of Borwein, Burke, Lewis, and
Wang to mappings with values in metric (resp. ordered normed linear)
spaces. We define two classes of monotone mappings between an ordered
linear space and a metric space (resp. ordered linear space):
$K$-monotone dominated and cone-to-cone monotone mappings. First
we show some relationships between these classes. Then, we study
continuity and differentiability (also in the metric and $w^*$
senses) of mappings in these classes.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46T20; 26B25
Remarks: 13 page; better abstract
The source file(s), domdif_prep.tex: 55009 bytes, is(are) stored
in gzipped form as 0510678.gz with size 16kb. The corresponding
postcript file has gzipped size 56kb.
Submitted from: jakub.duda at weizmann.ac.il
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0510678
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From alspach at www.math.okstate.edu Thu Nov 3 07:16:31 2005
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200511031316.jA3DGU4c039900 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Bas Lemmens, Beata Randrianantoanina, and Onno van Gaans
Status: R
This is an announcement for the paper "Second derivatives of norms
and contractive complementation in vector-valued spaces" by Bas
Lemmens, Beata Randrianantoanina, and Onno van Gaans.
Abstract: We consider 1-complemented subspaces (ranges of contractive
projections) of vector-valued spaces $\ell_p(X)$, where $X$ is a
Banach space with a 1-unconditional basis and $p \in (1,2)\cup
(2,\infty)$. If the norm of $X$ is twice continuously differentiable
and satisfies certain conditions connecting the norm and the notion
of disjointness with respect to the basis, then we prove that every
1-complemented subspace of $\ell_p(X)$ admits a basis of mutually
disjoint elements. Moreover, we show that every contractive projection
is then an averaging operator. We apply our results to the space
$\ell_p(\ell_q)$ with $p,q\in (1,2)\cup (2,\infty)$ and obtain a
complete characterization of its 1-complemented subspaces.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B45, 46B04 (Primary) 47B37
(Secondary)
Remarks: 22 pages, LaTeX
The source file(s), lplqsub.tex: 52714 bytes, is(are) stored in
gzipped form as 0511044.gz with size 15kb. The corresponding postcript
file has gzipped size 80kb.
Submitted from: lemmens at maths.warwick.ac.uk
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0511044
or
http://arXiv.org/abs/math.FA/0511044
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From alspach at www.math.okstate.edu Mon Nov 7 06:25:06 2005
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200511071225.jA7CP5bI024658 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Aaron Zerhusen
Status: R
This is an announcement for the paper "An embedding theorem for
pseudoconvex domains in Banach spaces" by Aaron Zerhusen.
Abstract: We show that a pseudoconvex open subset of a Banach space
with an unconditional basis is biholomorphic to a closed direct
submanifold of a Banach space with an unconditional basis.
Archive classification: Complex Variables; Functional Analysis
Mathematics Subject Classification: 32T; 46G20
Remarks: 14 pages
The source file(s), zerhusen.tex: 30421 bytes, is(are) stored in
gzipped form as 0511095.gz with size 10kb. The corresponding postcript
file has gzipped size 60kb.
Submitted from: azerhus at math.purdue.edu
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.CV/0511095
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From alspach at www.math.okstate.edu Tue Nov 8 15:13:29 2005
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Date: Tue, 8 Nov 2005 15:13:29 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200511082113.jA8LDTLl004536 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Valentin Ferenczi
Status: R
This is an announcement for the paper "Real hereditarily indecomposable
Banach spaces and uniqueness of complex structure" by Valentin
Ferenczi.
Abstract: There exists a real hereditarily indecomposable Banach
space $X$ such that the quotient space $L(X)/S(X)$ by strictly
singular operators is isomorphic to the complex field (resp. to the
quaternionic division algebra).
Up to isomorphism, the example with complex quotient space has
exactly two complex structures, which are conjugate, totally
incomparable, and both hereditarily indecomposable; this extends
results of J. Bourgain and S. Szarek from 1986.
The quaternionic example, on the other hand, has unique complex
structure up to isomorphism; there also exists a space with an
unconditional basis, non isomorphic to $l_2$, which admits a unique
complex structure. These examples answer a question of Szarek.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B03; 46B04; 47B99
Remarks: 29 pages
The source file(s), cplexstructure_ferenczi.tex: 70811 bytes, is(are)
stored in gzipped form as 0511166.gz with size 22kb. The corresponding
postcript file has gzipped size 87kb.
Submitted from: ferenczi at ccr.jussieu.fr
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0511166
or
http://arXiv.org/abs/math.FA/0511166
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uget 0511166
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200511082115.jA8LFTIJ004596 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Valentin Ferenczi
Status: R
This is an announcement for the paper "On the number of non
permutatively equivalent sequences in a Banach space" by Valentin
Ferenczi.
Abstract: This paper contains results concerning the Borel reduction
of the relation $E_0$ of eventual agreement between sequences of
$0$'s and $1$'s, to the relation of permutative equivalence between
basic sequences in a Banach space. For more clarity in this abstract,
we state these results in terms of classification by real numbers.
If $R$ is some (analytic) equivalence relation on a Polish space
$X$, it is said that $R$ is classifiable (by real numbers) if there
exists a Borel map $g$ from $X$ into the real line such that $x R
x'$ if and only if $g(x)=g(x')$. If $R$ is not classifiable, there
must be $2^{\omega}$ $R$-classes. It is conjectured that any separable
Banach space such that isomorphism between its subspaces is
classifiable must be isomorphic to $l_2$.
We prove the following results: - the relation $\sim^{perm}$ of
permutative equivalence between normalized basic sequences is
analytic non Borel,
- if $X$ is a Banach space with a Schauder basis $(e_n)$, such
that $\sim^{perm}$ between normalized block-sequences of $X$ is
classifiable, then $X$ is $c_0$ or $\ell_p$ saturated for some $1
\leq p <+\infty$,
- if $(e_n)$ is shrinking unconditional, and $\sim^{perm}$ between
normalized disjointly supported sequences in $X$, resp. in $X^*$,
are classifiable, then $(e_n)$ is equivalent to the unit vector
basis of $c_0$ or $\ell_p$,
- if $(e_n)$ is unconditional, then either $X$ is isomorphic to
$l_2$, or $X$ contains $2^{\omega}$ subspaces or $2^{\omega}$
quotients which are spanned by pairwise non permutatively equivalent
normalized unconditional bases.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B03; 03E15
Remarks: 28 pages
The source file(s), permutative_ferenczi.tex: 72505 bytes, is(are)
stored in gzipped form as 0511170.gz with size 21kb. The corresponding
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Submitted from: ferenczi at ccr.jussieu.fr
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0511170
or
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From banach-bounces at math.okstate.edu Thu Nov 10 08:28:11 2005
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Date: Thu, 10 Nov 2005 08:26:03 -0600
From: Dale Alspach <alspach at math.okstate.edu>
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Subject: [Banach] Activities In honor of Bill Johnson's 60th Birthday
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Status: R
In honor of Bill Johnson's 60th birthday we have organized an /AMS
Special Session on Extension of Functions/
<http://www.ams.org/amsmtgs/2095_program_ss5.html#title> at the 2006
Joint Mathematics Meeting in San Antonio, Texas.
There will be a banquet on Thursday, January 12, at Biga's on the Bank
<http://www.biga.com/> (*located on the River Walk, 203 South St. Mary's
St, San Antonio, Texas 78205* ) starting at 7:00 pm. Biga's is a
modern-American restaurant and its menu is inspired by the cuisines of
Mexico and Asia. The price of the banquet is $20.00 and it is being
supported in part by Texas A&M University. Please note that space is
limited for the banquet and we are asking for attendees to register for
it in advance. If you plan to attend, please send an email message to
any of us
Alvaro Arias aarias at math.du.edu <mailto:aarias at math.du.edu>
Edward W. Odell odell at math.utexas.edu <mailto:odell at math.utexas.edu>
Thomas Schlumprecht schlump at math.tamu.edu <mailto:schlump at math.tamu.edu>
You can find more information at the website
www.math.du.edu/~aarias/bill.htm
_______________________________________________
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Date: Wed, 9 Nov 2005 23:04:25 -0500
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From: "Stanislaw J. Szarek" <sjs13 at po.cwru.edu>
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Subject: [Banach] Positions at Case
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Status: R
(This announcement, with additional active hyperlinks, is also accessible via
http://www.case.edu/artsci/dean/searches/ )
The Department of Mathematics in the College of Arts & Sciences at
Case Western Reserve University invites applications for one or more
faculty positions. Although rank is open and commensurate with
qualifications, we prefer to appoint at the rank of assistant
professor. We especially emphasize coordination with Department,
College and University goals, including undergraduate teaching in the
University's SAGES (Seminar Approach to General Education and
Scholarship) program. Areas of preference identified to complement
existing department activities include:
(1) Functional analysis, convexity theory and related
high-dimensional phenomena, the area that recently has been often
referred to as "asymptotic geometric analysis" and of which members
of the Department are internationally recognized leaders. See
http://www.cwru.edu/artsci/math/szarek/ and
http://www.cwru.edu/artsci/math/werner/ for examples of recent
research directions. Besides hires that would directly augment this
research, the Department envisions expanding into related areas of
non-commutative geometry/functional analysis or even theoretical
computer science or complexity theory.
(2) Probability theory. Areas currently represented in the
Department include large deviation theory and stochastic differential
equations. As indicated on our website, the Department has
researchers in a number of mathematical fields, and a candidate's
potential ability to interact and collaborate with colleagues in
other areas of mathematics will be regarded as a valuable asset.
Candidates are invited to address this point. Case has strong
presences in biomedical, engineering and other scientific areas and,
in addition to strong theoretical credentials, a candidate's
potential ability to interact and collaborate with colleagues in
other disciplines will also be regarded as a valuable asset.
Notwithstanding the above, (3) exceptionally strong candidates in
other areas will be considered. Depending on needs, (4) visiting
positions/instructorships/lectureships may also be open.
Indicate in which area you wish to be considered. The successful
candidate will hold the Ph.D. or equivalent (Masters for lectureship)
and have, relative to career stage, a distinguished record of
publication, research, service, and teaching. Compensation
commensurate with qualifications.
Case is an integral part of one of the major research medical
complexes in the country. It also has a major presence in various
science and engineering disciplines. Geographically, it is located on
the eastern edge of Cleveland, in northeast Ohio, adjacent to
University Circle, home to the Cleveland Symphony Orchestra, the
Cleveland Museum of Art, and many other cultural institutions. There
is a wide variety of housing, schooling, and other amenities nearby.
The Department has approximately 20 faculty, with several focused
research areas. The Department is responsible for service (beginning
with calculus), majors, and graduate instruction. Nominal teaching
load is 2/2. The Department has a dedicated 8 CPU computational
server with an SGI 3D graphics front end. Facilities of the Ohio
Supercomputer Center are also available.
Electronic applications only, to: James Alexander,
math-faculty-position at case.edu, consisting of a letter of
application, which indicates in which area of preference you wish to
be considered, AMS cover sheet, a c.v., and the names and contact
information for four referees to whom we may write. Evaluation of
applications will begin December 15, 2005. Case is a recipient of a
National Science Foundation ADVANCE institutional transformation
grant to increase the participation of women in science and
engineering. Case Western Reserve University is committed to
diversity and is an affirmative action, equal opportunity employer.
Applications from women or minorities are especially encouraged.
_______________________________________________
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From alspach at www.math.okstate.edu Sat Nov 19 19:29:59 2005
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200511200129.jAK1Twnu003289 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Julien Melleray
Status: R
This is an announcement for the paper "Computing the complexity of
the relation of isometry between separable Banach spaces" by
Julien Melleray.
Abstract: We compute here the Borel complexity of the relation of
isometry between separable Banach spaces, using results of Gao,
Kechris and Weaver.
Archive classification: Functional Analysis; Logic
Mathematics Subject Classification: 03E15
The source file(s), melleray_banachisometries.tex: 34260 bytes,
is(are) stored in gzipped form as 0511456.gz with size 11kb. The
corresponding postcript file has gzipped size 54kb.
Submitted from: melleray at math.jussieu.fr
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0511456
or
http://arXiv.org/abs/math.FA/0511456
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uget 0511456
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From alspach at www.math.okstate.edu Mon Dec 5 07:21:24 2005
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Date: Mon, 5 Dec 2005 07:21:24 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200512051321.jB5DLORb059094 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jakub Duda
Status: R
This is an announcement for the paper "On Gateaux differentiability
of pointwise Lipschitz mappings" by Jakub Duda.
Abstract: We prove that for every function $f:X\to Y$, where $X$
is a separable Banach space and $Y$ is a Banach space with RNP,
there exists a set $A\in\tilde\mcA$ such that $f$ is Gateaux
differentiable at all $x\in S(f)\setminus A$, where $S(f)$ is the
set of points where $f$ is pointwise-Lipschitz. This improves a
result of Bongiorno. As a corollary, we obtain that every $K$-monotone
function on a separable Banach space is Hadamard differentiable
outside of a set belonging to $\tilde\mcC$; this improves a result
due to Borwein and Wang. Another corollary is that if $X$ is
Asplund, $f:X\to\R$ cone monotone, $g:X\to\R$ continuous convex,
then there exists a point in $X$, where $f$ is Hadamard differentiable
and $g$ is Frechet differentiable.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46G05; 46T20
Remarks: 11 pages; added name
The source file(s), stronger_stepanoff.tex: 48652 bytes, is(are)
stored in gzipped form as 0511565.gz with size 15kb. The corresponding
postcript file has gzipped size 61kb.
Submitted from: jakub.duda at weizmann.ac.il
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0511565
or
http://arXiv.org/abs/math.FA/0511565
or by email in unzipped form by transmitting an empty message with
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uget 0511565
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From alspach at www.math.okstate.edu Mon Dec 5 07:24:28 2005
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Date: Mon, 5 Dec 2005 07:24:28 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200512051324.jB5DOSsk059152 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Manor Mendel and Assaf Naor
Status: R
This is an announcement for the paper "Ramsey partitions and proximity
data structures" by Manor Mendel and Assaf Naor.
Abstract: This paper addresses two problems lying at the intersection
of geometric analysis and theoretical computer science: The non-linear
isomorphic Dvoretzky theorem and the design of good approximate
distance oracles for large distortion. We introduce the notion of
Ramsey partitions of a finite metric space, and show that the
existence of good Ramsey partitions implies a solution to the metric
Ramsey problem for large distortion (a.k.a. the non-linear version
of the isomorphic Dvoretzky theorem, as introduced by Bourgain,
Figiel, and Milman in \cite{BFM86}). We then proceed to construct
optimal Ramsey partitions, and use them to show that for every
$\e\in (0,1)$, any $n$-point metric space has a subset of size
$n^{1-\e}$ which embeds into Hilbert space with distortion $O(1/\e)$.
This result is best possible and improves part of the metric Ramsey
theorem of Bartal, Linial, Mendel and Naor \cite{BLMN05}, in addition
to considerably simplifying its proof. We use our new Ramsey
partitions to design the best known approximate distance oracles
when the distortion is large, closing a gap left open by Thorup and
Zwick in \cite{TZ05}. Namely, we show that for any $n$ point metric
space $X$, and $k\geq 1$, there exists an $O(k)$-approximate distance
oracle whose storage requirement is $O(n^{1+1/k})$, and whose query
time is a universal constant. We also discuss applications of Ramsey
partitions to various other geometric data structure problems, such
as the design of efficient data structures for approximate ranking.
Archive classification: Data Structures and Algorithms; Computational
Geometry; Metric Geometry; Functional Analysis
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. The corresponding postcript file has gzipped size .
Submitted from: anaor at microsoft.com
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/cs.DS/0511084
or
http://arXiv.org/abs/cs.DS/0511084
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From alspach at www.math.okstate.edu Mon Dec 5 07:25:26 2005
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Date: Mon, 5 Dec 2005 07:25:26 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200512051325.jB5DPQ9Q059196 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Emanuel Milman
Status: R
This is an announcement for the paper "Generalized intersection
bodies" by Emanuel Milman.
Abstract: We study the structures of two types of generalizations
of intersection-bodies and the problem of whether they are in fact
equivalent. Intersection-bodies were introduced by Lutwak and
played a key role in the solution of the Busemann-Petty problem. A
natural geometric generalization of this problem considered by
Zhang, led him to introduce one type of generalized intersection-bodies.
A second type was introduced by Koldobsky, who studied a different
analytic generalization of this problem. Koldobsky also studied the
connection between these two types of bodies, and noted that an
equivalence between these two notions would completely settle the
unresolved cases in the generalized Busemann-Petty problem. We show
that these classes share many identical structure properties, proving
the same results using Integral Geometry techniques for Zhang's
class and Fourier transform techniques for Koldobsky's class. Using
a Functional Analytic approach, we give several surprising equivalent
formulations for the equivalence problem, which reveal a deep
connection to several fundamental problems in the Integral Geometry
of the Grassmann Manifold.
Archive classification: Functional Analysis; Geometric Topology;
Metric Geometry
Remarks: 44 pages
The source file(s), generalized-intersection-bodies-for-arxiv.bbl:
6010 bytes, generalized-intersection-bodies-for-arxiv.tex: 129282
bytes, is(are) stored in gzipped form as 0512058.tar.gz with size
38kb. The corresponding postcript file has gzipped size 159kb.
Submitted from: emanuel.milman at weizmann.ac.il
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0512058
or
http://arXiv.org/abs/math.FA/0512058
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From banach-bounces at math.okstate.edu Thu Dec 8 08:37:54 2005
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Date: Wed, 7 Dec 2005 20:24:20 -0500 (EST)
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Subject: [Banach] CBMS conference on A Probabalistic and Combinatorial
Approach in Analysis
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Status: R
Dear Friends,
In August 2006 (from the 6th to the 13th, to be precise), the Department
of Mathematical Science of Kent State University will be hosting a CBMS
conference, 'A Probabilistic and Combinatorial Approach in Analysis', with
Professor Mark Rudelson from the University of Missouri as the main
speaker. We hope that you will be able to participate.
With CBMS funding we will be able to cover local expenses for a limited
number of participants, so it is advisable to reply as soon as possible
to Artem Zvavitch (zvavitch at math.kent.edu). At this time, we have very
limited funding for travel; to be as efficient as possible in the use of
the available travel funds, we encourage you to encourage your graduate
students and postdocs to participate, as well.
For further information and breaking news a look at
http://www.math.kent.edu/math/CBMS.cfm
is advised.
Please note that your early response will help us gauge the needs for
housing, lecture room(s), etc. We hope to be sending out information
regarding housing by the end of December.
HOPE TO SEE YOU IN KENT NEXT AUGUST!!
Best Regards,
Richard Aron, Joe Diestel, Per Enflo, Victor Lomonosov, Andrew Tonge, and
Artem Zvavitch
_______________________________________________
Banach mailing list
Banach at math.okstate.edu
http://mail.math.okstate.edu/mailman/listinfo/banach
From alspach at www.math.okstate.edu Tue Dec 13 11:51:17 2005
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Date: Tue, 13 Dec 2005 11:51:16 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200512131751.jBDHpGYj012118 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Emanuel Milman
Status: R
This is an announcement for the paper "Dual mixed volumes and the
slicing problem" by Emanuel Milman.
Abstract: We develop a technique using dual mixed-volumes to study
the isotropic constants of some classes of spaces. In particular,
we recover, strengthen and generalize results of Ball and Junge
concerning the isotropic constants of subspaces and quotients of
L_p and related spaces. An extension of these results to negative
values of p is also obtained, using generalized intersection-bodies.
In particular, we show that the isotropic constant of a convex body
which is contained in an intersection-body is bounded (up to a
constant) by the ratio between the latter's mean-radius and the
former's volume-radius. We also show how type or cotype 2 may be
used to easily prove inequalities on any isotropic measure.
Archive classification: Functional Analysis; Metric Geometry
Remarks: 38 pages, to appear in Advance in Mathematics
The source file(s), dual-mixed-volumes-and-slicing-problem-for-arxiv.bbl:
7985 bytes, dual-mixed-volumes-and-slicing-problem-for-arxiv.tex:
94404 bytes, is(are) stored in gzipped form as 0512207.tar.gz with
size 29kb. The corresponding postcript file has gzipped size 130kb.
Submitted from: emanuel.milman at weizmann.ac.il
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0512207
or
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From alspach at www.math.okstate.edu Tue Dec 13 11:51:55 2005
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Date: Tue, 13 Dec 2005 11:51:55 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200512131751.jBDHptka012149 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Emanuel Milman
Status: R
This is an announcement for the paper "A comment on the low-dimensional
Busemann-Petty problem" by Emanuel Milman.
Abstract: The generalized Busemann-Petty problem asks whether
centrally-symmetric convex bodies having larger volume of all
m-dimensional sections necessarily have larger volume. When m>3
this is known to be false, but the cases m=2,3 are still open. In
those cases, it is shown that when the smaller body's radial function
is a (n-m)-th root of the radial function of a convex body, the
answer to the generalized Busemann-Petty problem is positive (for
any larger star-body). Several immediate corollaries of this
observation are also discussed.
Archive classification: Functional Analysis; Metric Geometry
Remarks: 9 pages, to appear in GAFA Seminar Notes
The source file(s), low-dim-BP-problem.bbl: 4623 bytes,
low-dim-BP-problem.tex: 24305 bytes, is(are) stored in gzipped form
as 0512208.tar.gz with size 10kb. The corresponding postcript file
has gzipped size 53kb.
Submitted from: emanuel.milman at weizmann.ac.il
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0512208
or
http://arXiv.org/abs/math.FA/0512208
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uget 0512208
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From alspach at www.math.okstate.edu Wed Dec 14 16:19:42 2005
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Date: Wed, 14 Dec 2005 16:19:42 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200512142219.jBEMJgAl025390 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Assaf Naor and Gideon Schechtman
Status: R
This is an announcement for the paper "Planar earthmover is not in
$L_1$" by Assaf Naor and Gideon Schechtman.
Abstract: We show that any $L_1$ embedding of the transportation
cost (a.k.a. Earthmover) metric on probability measures supported
on the grid $\{0,1,...,n\}^2\subseteq \R^2$ incurs distortion
$\Omega(\sqrt{\log n})$. We also use Fourier analytic techniques
to construct a simple $L_1$ embedding of this space which has
distortion $O(\log n)$.
Archive classification: Computational Geometry; Functional Analysis
The source file(s), , is(are) stored in gzipped form as with size
. The corresponding postcript file has gzipped size .
Submitted from: anaor at microsoft.com
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/cs.CG/0509074
or
http://arXiv.org/abs/cs.CG/0509074
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From alspach at www.math.okstate.edu Thu Dec 15 08:21:44 2005
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Date: Thu, 15 Dec 2005 08:21:44 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200512151421.jBFELiCk034585 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Catalin Badea and Vladimir Mueller
Status: R
This is an announcement for the paper "Growth conditions and inverse
producing extensions" by Catalin Badea and Vladimir Mueller.
Abstract: We study the invertibility of Banach algebras elements
in their extensions, and invertible extensions of Banach and Hilbert
space operators with prescribed growth conditions for the norm of
inverses. As applications, the solutions of two open problems are
obtained. In the first one we give a characterization of E(T)-subscalar
operators in terms of growth conditions. In the second one we show
that operators satisfying a Beurling-type growth condition possess
Bishop's property beta. Other applications are also given.
Archive classification: Functional Analysis; Operator Algebras
Remarks: 22 pages
The source file(s), bm1arx.tex: 60879 bytes, is(are) stored in
gzipped form as 0512321.gz with size 19kb. The corresponding postcript
file has gzipped size 90kb.
Submitted from: catalin.badea at math.univ-lille1.fr
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0512321
or
http://arXiv.org/abs/math.FA/0512321
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From banach-bounces at math.okstate.edu Tue Dec 20 17:19:05 2005
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Date: Tue, 20 Dec 2005 17:19:03 -0600
From: Dale Alspach <alspach at math.okstate.edu>
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Subject: [Banach] Nicole Tomczak-Jaegerman: Recipient of the 2006
CRM-Fields-PIMS Prize
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(From PIMS)
NICOLE TOMCZAK-JAEGERMAN: RECIPIENT OF THE 2006 CRM-FIELDS-PIMS PRIZE
The directors of the Centre de recherches mathematiques (CRM) of
l'Universite de Montreal - Francois Lalonde, the Fields Institute -
Barbara Keyfitz, and the Pacific Institute for the Mathematical
Sciences - Ivar Ekeland, are pleased to announce the awarding of the
CRM-Fields-PIMS Prize for 2006 to Professor Nicole Tomczak-Jaegermann
of the University of Alberta in recognition of her exceptional
achievements in functional analysis and geometric analysis.
The prize was established in 1994 as the CRM-Fields prize to recognize
exceptional research in the mathematical sciences. In 2005, PIMS
became an equal partner and the name was changed to the
CRM-Fields-PIMS prize. A committee appointed by the three institutes
chooses the recipient.
Nicole Tomczak-Jaegermann, this year's recipient, is one of the
world's leading mathematicians working in functional analysis. She
has made outstanding contributions to infinite dimensional Banach
space theory, asymptotic geometric analysis, and the interaction
between these two streams of modern functional analysis.
She holds a Canada Research Chair in Geometric Analysis at the
University of Alberta. In 1998 she gave an invited lecture at the
International Congress of Mathematicians, is a Fellow of the Royal
Society of Canada, received a Killam Research Fellowship, and the
Krieger-Nelson Prize Lectureship of the Canadian Mathematical Society.
Previous recipients of the prize are H.S.M. (Donald) Coxeter, George
A. Elliott, James Arthur, Robert V. Moody, Stephen A. Cook, Israel
Michael Sigal, William T. Tutte, John B. Friedlander, John McKay,
Edwin Perkins, Donald A. Dawson, and David Boyd.
For more information please see
http://www.pims.math.ca
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Date: Wed, 21 Dec 2005 11:28:53 -0500 (EST)
From: "Mario M. Milman" <milman at fau.edu>
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Subject: [Banach] Interpolation Theory and Applications: A Conference in
Honor of Michael Cwikel
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Status: R
Interpolation Theory and Applications: A Conference in Honor of Michael
Cwikel
More information:
http://www.ams.org/mathcal/info/2006_mar29-31_coralgables.html
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