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October, 2007 Weakly exact von Neumann algebras
Narutaka OZAWA
J. Math. Soc. Japan 59(4): 985-991 (October, 2007). DOI: 10.2969/jmsj/05940985

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.

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Narutaka OZAWA. "Weakly exact von Neumann algebras." J. Math. Soc. Japan 59 (4) 985 - 991, October, 2007. https://doi.org/10.2969/jmsj/05940985

Information

Published: October, 2007
First available in Project Euclid: 10 December 2007

zbMATH: 1137.46034
MathSciNet: MR2370001
Digital Object Identifier: 10.2969/jmsj/05940985

Subjects:
Primary: 46L10
Secondary: 46L07

Keywords: weakly exact von Neumann algebras

Rights: Copyright © 2007 Mathematical Society of Japan

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Vol.59 • No. 4 • October, 2007
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