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@uam.es

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

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

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