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

Marius Junge·Javier Parcet
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Abstract

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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Marius Junge, Javier Parcet. 2004-07-28. The norm of sums of independent noncommutative random variables in $L_p(\ell_1)$. https://arxiv.org/abs/math/0403103

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