Weakly Exact von Neumann Algebras
Operator Algebras
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0411473,
title = {Weakly Exact von Neumann Algebras},
author = {Narutaka Ozawa},
journal= {arXiv preprint arXiv:math/0411473},
year = {2007}
}
Comments
8 pages