The norm of sums of independent noncommutative random variables in $L_p(\ell_1)$

Details The norm of sums of independent noncommutative random variables in $L_p(\ell_1)$ The norm of sums of independent noncommutative random variables in $L_p(\ell_1)$

2004-03-05

arxiv.org/abs/math/0403103v2

Mathematics

Functional Analysis

30 pages. To appear in J. Funct. Anal

Scientific paper

We investigate the norm of sums of independent vector-valued random variables in noncommutative 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.

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