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

Rui Okayasu, Reiji Tomatsu

研究成果: Article査読

1 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)259-288
ページ数30
ジャーナルJournal of Operator Theory
75
2
DOI
出版ステータスPublished - 2016
外部発表はい

ASJC Scopus subject areas

  • Algebra and Number Theory

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