Journal of the Mathematical Society of Japan

Weakly exact von Neumann algebras

Narutaka OZAWA

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.

Article information

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

Dates
First available in Project Euclid: 10 December 2007

https://projecteuclid.org/euclid.jmsj/1197320623

Digital Object Identifier
doi:10.2969/jmsj/05940985

Mathematical Reviews number (MathSciNet)
MR2370001

Zentralblatt MATH identifier
1137.46034

Citation

OZAWA, Narutaka. Weakly exact von Neumann algebras. J. Math. Soc. Japan 59 (2007), no. 4, 985--991. doi:10.2969/jmsj/05940985. https://projecteuclid.org/euclid.jmsj/1197320623

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