The norm of sums of independent noncommutative random variables in Lp(ℓ1)

Marius Junge, Javier Parcet

Research output: Contribution to journalArticlepeer-review

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 Sqn in Sp (ℓq m) with optimal order m ∼ n2. 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.

Original languageEnglish (US)
Pages (from-to)366-406
Number of pages41
JournalJournal of Functional Analysis
Volume221
Issue number2
DOIs
StatePublished - Apr 15 2005
Externally publishedYes

Keywords

  • K-convexity
  • Noncommutative random variable
  • Operator space
  • Type and cotype

ASJC Scopus subject areas

  • Analysis

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