Haagerup approximation property and positive cones associated with a von Neumann Algebra

Rui Okayasu, Reiji Tomatsu

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We introduce the notion of the a-Haagerup approximation property (α-HAP) for α ∈ [0, 1/2] using a one-parameter family of positive cones studied by Araki and show that the a-HAP actually does not depend on the choice of α. This enables us to prove the fact that the Haagerup approximation properties introduced in two ways are actually equivalent, one in terms of the standard form and the other in terms of completely positive maps. We also discuss the Lp-Haagerup approximation property (Lp-HAP) for a noncommutative Lp-space associated with a von Neumann algebra for p ∈ (1,∞) and show the independence of the Lp-HAP on the choice of p.

Original languageEnglish
Pages (from-to)259-288
Number of pages30
JournalJournal of Operator Theory
Volume75
Issue number2
DOIs
Publication statusPublished - 2016
Externally publishedYes

Keywords

  • Haagerup approximation property
  • Non-commutative L-space
  • von Neumann algebra

ASJC Scopus subject areas

  • Algebra and Number Theory

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