Weakly Exact von Neumann Algebras

Details Weakly Exact von Neumann Algebras Weakly Exact von Neumann Algebras

2004-11-22

arxiv.org/abs/math/0411473v1

Mathematics

Operator Algebras

8 pages

Scientific paper

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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