Tracially Z-absorbing C*-algebras

Ilan Hirshberg; Joav Orovitz

doi:10.1016/j.jfa.2013.05.005

Tracially Z-absorbing C^*-algebras

Research output: Contribution to journal › Article › peer-review

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≅A≉Z. We furthermore show that this property is preserved under forming certain crossed products by actions satisfying a tracial Rokhlin type property.

Original language	English
Pages (from-to)	765-785
Number of pages	21
Journal	Journal of Functional Analysis
Volume	265
Issue number	5
DOIs	https://doi.org/10.1016/j.jfa.2013.05.005
State	Published - 1 Sep 2013
Externally published	Yes

Bibliographical note

Funding Information:
* Corresponding author. E-mail addresses: [email protected] (I. Hirshberg), [email protected] (J. Orovitz). 1 This research was supported in part by Israel Science Foundation grant 1471/07.

Keywords

C-algebras
Rokhlin property

ASJC Scopus subject areas

Analysis

Access to Document

10.1016/j.jfa.2013.05.005

Cite this

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title = "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≅A≉Z. We furthermore show that this property is preserved under forming certain crossed products by actions satisfying a tracial Rokhlin type property.",

keywords = "C-algebras, Rokhlin property",

author = "Ilan Hirshberg and Joav Orovitz",

note = "Funding Information: * Corresponding author. E-mail addresses: [email protected] (I. Hirshberg), [email protected] (J. Orovitz). 1 This research was supported in part by Israel Science Foundation grant 1471/07.",

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AB - 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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KW - Rokhlin property

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