[Banach] Abstract of a paper by Stanislaw J. Szarek, and Nicole Tomczak-Jaegermann
alspach at www.math.okstate.edu
Thu Jul 15 07:14:39 CDT 2004
This is an announcement for the paper "Saturating constructions for
normed spaces" by Stanislaw J. Szarek and Nicole Tomczak-Jaegermann .
Abstract: We prove several results of the following type: given finite
dimensional normed space V there exists another space X with
log(dim X) = O(log(dim V)) and such that every subspace (or quotient) of X,
whose dimension is not "too small," contains a further subspace isometric
to V. This sheds new light on the structure of such large subspaces or
quotients (resp., large sections or projections of convex bodies) and
allows to solve several problems stated in the 1980s by V. Milman. The
proofs are probabilistic and depend on careful analysis of images of
convex sets under Gaussian linear maps.
Archive classification: Functional Analysis; Probability
Mathematics Subject Classification: 46B20; 52A21; 52A22; 60D05
Remarks: 27 p., LATEX
The source file(s), SzarekTomczakSat1.tex: 71711 bytes, is(are) stored
in gzipped form as 0407233.gz with size 25kb. The corresponding postcript
file has gzipped size 105kb.
Submitted from: szarek at cwru.edu
The paper may be downloaded from the archive by web browser from URL
or by email in unzipped form by transmitting an empty message with
or in gzipped form by using subject line
to: math at arXiv.org.
More information about the Banach