Tracially Z-absorbing C*-algebras
Operator Algebras
2013-05-02 v2
Abstract
We study a tracial notion of Z-absorption for simple, unital C*-algebras. We show that if A is a C*-algebra for which this property holds then A has almost unperforated Cuntz semigroup, and if in addition A is nuclear and separable we show this property is equivalent to having A being Z-absorbing. We furthermore show that this property is preserved under forming certain crossed products by actions satisfying a tracial Rokhlin type property.
Keywords
Cite
@article{arxiv.1208.2444,
title = {Tracially Z-absorbing C*-algebras},
author = {Ilan Hirshberg and Joav Orovitz},
journal= {arXiv preprint arXiv:1208.2444},
year = {2013}
}
Comments
17 pages. Minor revisions, to appear J. Funct. Anal