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Property T for general C*-algebras

Published online by Cambridge University Press:  29 November 2013

CHI–KEUNG NG
CHI–KEUNG NG*
Affiliation:
Chern Institute of Mathematics, Nankai University, Tianjin 300071, China. e-mail: [email protected]
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Abstract

In this paper, we extend the definition of property T and strong property T to general C*-algebras (not necessarily unital). We show that if an inclusion pair of locally compact groups (G,H) has property T, then (C*(G), C*(H)) has property T. As a partial converse, if T is abelian and C*(G) has property T, then T is compact. We also show that if Ω is a first countable locally compact Hausdorff space, then C0(Ω) has (strong) property T if and only if Ω is discrete. Furthermore, the non-unital C*-algebra $c_0(\mathbb{Z}^n)\rtimes SL_n(\mathbb{Z})$ has strong property T when n ≥ 3. We also give some equivalent forms of strong property T, which are new even in the unital case.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 156 , Issue 2 , March 2014 , pp. 229 - 239
Copyright
Copyright © Cambridge Philosophical Society 2013 

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