# [Banach] Abstract of a paper by Marius Junge and Javier Parcet

Dale Alspach alspach at www.math.okstate.edu
Tue Mar 9 06:34:59 CST 2004

This is an announcement for the paper "The norm of sums of independent
non-commutative random variables in   $L_p(\ell_1)$" by Marius Junge
and Javier Parcet.

Abstract: We investigate the norm of sums of independent vector-valued
random variables in non-commutative Lp spaces. This allows us to obtain
a uniform family of complete embeddings of the Schatten class Sq^n
in Sp(lq^m) with optimal order m=n^2. Using these embeddings we show
the surprising fact that the sharp type (cotype) index in the sense of
operator spaces for Lp[0,1] is min(p,p') (max(p,p')). Similar techniques
are used to show that the operator space notions of B-convexity and
K-convexity are equivalent.

Archive classification: Functional Analysis; Operator Algebras

Mathematics Subject Classification: 46L07; 46L52; 46L53

Remarks: 30 pages

The source file(s), Lp1.tex: 107978 bytes, is(are) stored in gzipped
form as 0403103.gz with size 29kb. The corresponding postcript file has
gzipped size 133kb.

Submitted from: javier.parcet at uam.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/math.FA/0403103

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http://arXiv.org/abs/math.FA/0403103

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uget 0403103

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