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≅A≉Z. We furthermore show that this property is preserved under forming certain crossed products by actions satisfying a tracial Rokhlin type property.
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* Corresponding author. E-mail addresses: email@example.com (I. Hirshberg), firstname.lastname@example.org (J. Orovitz). 1 This research was supported in part by Israel Science Foundation grant 1471/07.
- Rokhlin property
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