Annals of Functional Analysis

The weak Haagerup property for C-algebras

Qing Meng

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Abstract

We define and study the weak Haagerup property for C-algebras in this article. A C-algebra with the Haagerup property always has the weak Haagerup property. We prove that a discrete group has the weak Haagerup property if and only if its reduced group C-algebra also has that property. Moreover, we consider the permanence of the weak Haagerup property under a few canonical constructions of C-algebras.

Article information

Source
Ann. Funct. Anal., Volume 8, Number 4 (2017), 502-511.

Dates
Received: 25 November 2016
Accepted: 5 January 2017
First available in Project Euclid: 22 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.afa/1498096870

Digital Object Identifier
doi:10.1215/20088752-2017-0014

Mathematical Reviews number (MathSciNet)
MR3717172

Zentralblatt MATH identifier
06841331

Subjects
Primary: 46L05: General theory of $C^*$-algebras
Secondary: 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations [See also 46Lxx]

Keywords
$C^{*}$-algebra weak Haagerup property tracial state

Citation

Meng, Qing. The weak Haagerup property for $C^{*}$ -algebras. Ann. Funct. Anal. 8 (2017), no. 4, 502--511. doi:10.1215/20088752-2017-0014. https://projecteuclid.org/euclid.afa/1498096870


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