Israel Journal of Mathematics

, Volume 137, Issue 1, pp 1–33 | Cite as

On spectral characterizations of amenability

  • Claire Anantharaman-Delaroche


We show that a measuredG-space (X, μ), whereG is a locally compact group, is amenable in the sense of Zimmer if and only if the following two conditions are satisfied: the associated unitary representationπ X ofG intoL 2(X, μ) is weakly contained into the regular representationλ G and there exists aG-equivariant norm one projection fromL∞(X×X) ontoL∞(X). We give examples of ergodic discrete group actions which are not amenable, althoughπ X is weakly contained intoλ G.


Normal Subgroup Compact Group Unitary Representation Closed Subgroup Regular Representation 
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© Hebrew University 2003

Authors and Affiliations

  • Claire Anantharaman-Delaroche
    • 1
  1. 1.Département de MathématiquesUniversité d’OrléansOrléans Cedex 2France

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