Unconditional basic sequences and homogeneous hilbertian subspaces of non-commutative Lp spaces

Marius Junge, Timur Oikhberg

Research output: Contribution to journalArticle

Abstract

Suppose A is a von Neumann algebra with a normal faithful normalized trace T. We prove that if Eis a homogeneous Hilbertian subspace of LP(T) (1 ≤ p < ∞) such that the norms induced on E by Lp (τ) and L2(τ) are equivalent, then E is completely isomorphic to the subspace of Lp([0, 1]) spanned by Rademacher functions. Consequently, any homogeneous subspace of Lp(τ) is completely isomorphic to the span of Rademacher functions in Lp([0, 1]). In particular, this applies to the linear span of operators satisfying the canonical anti-commutation relations. We also show that the real interpolation space (R, C)θ,p embeds completely isomorphically into Lp(R.) (R is the hyperfinite II1 factor) for any 1 ≤ p < 2 and θ ε (0, 1). Indiana University Mathematics Journal

Original languageEnglish (US)
Pages (from-to)733-766
Number of pages34
JournalIndiana University Mathematics Journal
Volume56
Issue number2
DOIs
StatePublished - Jun 6 2007

Keywords

  • Completely unconditional bases
  • Homogenous hilbertian spaces
  • Noncommutative L spaces

ASJC Scopus subject areas

  • Mathematics(all)

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