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

  • YVES CORNULIER (a1) and ROMAIN TESSERA (a2)

Abstract

Let A be a locally compact abelian group, and H a locally compact group acting on A. Let G=HA 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.

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

  • YVES CORNULIER (a1) and ROMAIN TESSERA (a2)

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