Operator space embedding of schatten p-classes into von Neumann algebra preduals

Marius Junge, Javier Parcet

Research output: Contribution to journalArticle

Abstract

Let X1 and X2 be subspaces of quotients of R \oplus OH and C \oplus OH respectively. We use new free probability techniques to construct a completely isomorphic embedding of the Haagerup tensor product X1 ⊗h2 into the predual of a sufficiently large QWEP von Neumann algebra. As an immediate application, given any 1 < q ≤ 2, our result produces a completely isomorphic embedding of ℓ_q (equipped with its natural operator space structure) into L1(A) with A a QWEP von Neumann algebra.

Original languageEnglish (US)
Pages (from-to)522-551
Number of pages30
JournalGeometric and Functional Analysis
Volume18
Issue number2
DOIs
StatePublished - Jul 1 2008

Keywords

  • Free random variable
  • Noncommutative Lp space
  • Operator space

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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