The weak Haagerup property for C∗-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.