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Property $(T)$ and strong Property $(T)$ for unital $C^*$-algebras
- Publication Year :
- 2009
-
Abstract
- In this paper, we will give a thorough study of the notion of Property $(T)$ for $C^*$-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 $\rm II_1$-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 $C^*$-algebra.
- Subjects :
- Mathematics - Operator Algebras
Mathematics - Functional Analysis
46L05, 22D25
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.0901.1948
- Document Type :
- Working Paper