Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 59, Number 4 (2007), 985-991.
Weakly exact von Neumann algebras
The theory of exact -algebras was introduced by Kirchberg and has been influential in recent development of -algebras. A fundamental result on exact -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.
J. Math. Soc. Japan, Volume 59, Number 4 (2007), 985-991.
First available in Project Euclid: 10 December 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46L10: General theory of von Neumann algebras
Secondary: 46L07: Operator spaces and completely bounded maps [See also 47L25]
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