Open Access
may 2014 Notes on $C_0$-representations and the Haagerup property
Paul Jolissaint
Bull. Belg. Math. Soc. Simon Stevin 21(2): 263-274 (may 2014). DOI: 10.36045/bbms/1400592624


For any locally compact group $G$, we show the existence and uniqueness up to quasi-equivalence of a unitary $C_0$-representation $\pi_0$ of $G$ such that the coefficient functions of $C_0$-representations of $G$ are exactly the coefficient functions of $\pi_0$. The present work, strongly influenced by [4] (which dealt exclusively with discrete groups), leads to new characterizations of the Haagerup property: $G$ has that property if and only if the representation $\pi_0$ induces a $*$-isomorphism of $C^*(G)$ onto $C^*_{\pi_0}(G)$. When $G$ is discrete and countable, we also relate the Haagerup property to relative strong mixing properties in the sense of [9] of the group von Neumann algebra $L(G)$ into finite von Neumann algebras.


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Paul Jolissaint. "Notes on $C_0$-representations and the Haagerup property." Bull. Belg. Math. Soc. Simon Stevin 21 (2) 263 - 274, may 2014.


Published: may 2014
First available in Project Euclid: 20 May 2014

zbMATH: 1296.22006
MathSciNet: MR3211015
Digital Object Identifier: 10.36045/bbms/1400592624

Primary: 22D10 , 22D25
Secondary: 46L10

Keywords: $C^*$-Algebras , Følner sequences , Locally compact groups , Strong mixing , unitary representations , von Neumann algebras

Rights: Copyright © 2014 The Belgian Mathematical Society

Vol.21 • No. 2 • may 2014
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