## Annals of Functional Analysis

### The weak Haagerup property for $C^{*}$-algebras

Qing Meng

#### 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
Accepted: 5 January 2017
First available in Project Euclid: 22 June 2017

https://projecteuclid.org/euclid.afa/1498096870

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

Mathematical Reviews number (MathSciNet)
MR3717172

Zentralblatt MATH identifier
06841331

#### 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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