Tracially Z-absorbing C*-algebras

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.

17 pages. Minor revisions, to appear J. Funct. Anal

References in corpus (2)

• Completely positive maps of order zero
• Strongly self-absorbing C*-algebras are Z-stable

Cited by in corpus (1)

• The radius of comparison of the crossed product by a tracially strictly approximately inner action