Tracially Z-absorbing C*-algebras

By Ilan Hirshberg, Joav Orovitz. 2012

94 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0f097c9ea67bd01b2627a4876008865fb32cd89c

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In Algebra and Number Theory

1. David Kerr
2. G'abor Szab'o
3. Frederic Pierre Jean Latrémolière
4. A. Kavruk

In Mathematical Physics

1. David Kerr
2. G'abor Szab'o
3. Hanfeng Li
4. Ben Hayes
5. Xiangdong Ye
6. Eli Glasner
7. Frederic Pierre Jean Latrémolière
8. Wen Huang

Citations in the corpus

• Dimension, comparison, and almost finiteness (2017, methodology): “= 0 for all a1,a2 ∈A satisfying a1a2 = 0. We write - for the relation of Cuntz subequivalence. In order to verify Z-stability we will use the following result of Hirshberg and Orovitz (Theorem 4.1 of [19]). Theorem 12.1. Let Abe a simple separable unital nuclear C∗-algebra not isomorphic to C. Suppo”
• Almost Finiteness and the Small Boundary Property (2018, result): “e existence of order-zero completely positive contractive maps ϕ from matrix algebras into A such that the image of ϕ is approximately central and 1−ϕ(1) is small in the sense of Cuntz subequivalence [19].2 The most recent affirmation of this analogy is the work of Castillejos, Evington, Tikuisis, Whi”