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A characterization of relative Kazhdan property T for semidirect products with abelian groups

Published online by Cambridge University Press:  23 June 2010

YVES CORNULIER  and
ROMAIN TESSERA
YVES CORNULIER
Affiliation:
IRMAR, Campus de Beaulieu, 35042 Rennes CEDEX, France (email: yves.decornulier@univ-rennes1.fr)
ROMAIN TESSERA
Affiliation:
ÉNS Lyon, 46, allée d’Italie, 69364 Lyon CEDEX 07, France (email: romain.tessera@umpa.ens-lyon.fr)
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Abstract

Let A be a locally compact abelian group, and H a locally compact group acting on A. Let G=H⋉A be the semidirect product, assumed σ-compact. We prove that the pair (G,A) has Kazhdan’s property T if and only if the only countably approximable H-invariant mean on the Borel subsets of the Pontryagin dual , supported at the neighbourhood of the trivial character, is the Dirac measure.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 3 , June 2011 , pp. 793 - 805
Copyright
Copyright © Cambridge University Press 2010

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