Weakly exact von Neumann algebras



Journal of the Mathematical Society of Japan

Weakly exact von Neumann algebras

Narutaka OZAWA

Source: J. Math. Soc. Japan Volume 59, Number 4 (2007), 985-991.

Abstract

The theory of exact $C^{*}$-algebras was introduced by Kirchberg and has been influential in recent development of $C^{*}$-algebras. A fundamental result on exact $C^{*}$-algebras is a local characterization of exactness. The notion of weakly exact von Neumann algebras was also introduced by Kirchberg. In this paper, we give a local characterization of weak exactness. As a corollary, we prove that a discrete group is exact if and only if its group von Neumann algebra is weakly exact. The proof naturally involves the operator space duality.

Primary Subjects: 46L10
Secondary Subjects: 46L07
Keywords: weakly exact von Neumann algebras

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1197320623
Digital Object Identifier: doi:10.2969/jmsj/05940985
Mathematical Reviews number (MathSciNet): MR2370001


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