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On spectral characterizations of amenability

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Abstract

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.

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Authors and Affiliations

  1. Département de Mathématiques, Université d’Orléans, B. P. 6759, F-45067, Orléans Cedex 2, France

    Claire Anantharaman-Delaroche

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  1. Claire Anantharaman-Delaroche
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Anantharaman-Delaroche, C. On spectral characterizations of amenability. Isr. J. Math. 137, 1–33 (2003). https://doi.org/10.1007/BF02785954

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  • DOI: https://doi.org/10.1007/BF02785954

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