Tracially Z-absorbing C*-algebras

2012/08/12 by Ilan Hirshberg, Hirshberg, Ilan, Joav Orovitz +1 · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1208.2444

openalex publication_date 2012/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Crossed products by compact group actions with the weak tracial Rokhlin property

Related

• Simple tracially Z-absorbing C*-algebras
• Group actions on simple tracially Z-absorbing C*-algebras
• Centrally Large Subalgebras and Tracial Z-Absorption
• The Jiang-Su absorption for inclusions of unital C*-algebras
• Actions of amenable groups and crossed products of Z-absorbing C*-algebras