## Annals of Functional Analysis

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

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

#### Abstract

We define and study the weak Haagerup property for ${C}^{\ast}$-algebras in this article. A ${C}^{\ast}$-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 ${C}^{\ast}$-algebra also has that property. Moreover, we consider the permanence of the weak Haagerup property under a few canonical constructions of ${C}^{\ast}$-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