Property $(T)$ and strong Property $(T)$ for unital $C^{\ast }$-algebras

Abstract

In this paper, we will give a thorough study of the notion of Property $(T)$ for $C^{\ast }$-algebras (as introduced by M.B. Bekka in \cite{Bek-T}) as well as a slight stronger version of it, called "strong property $(T)$" (which is also an analogue of the corresponding concept in the case of discrete groups and type $\mathrm{I}{\mathrm{I}}_1$-factors). More precisely, we will give some interesting equivalent formulations as well as some permanence properties for both property $(T)$ and strong property $(T)$. We will also relate them to certain $(T)$-type properties of the unitary group of the underlying $C^{\ast }$-algebra.

Cited by in corpus (1)

• Property $T$ of reduced $C^{\ast }$-crossed products by discrete groups