On spectral characterizations of amenability
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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.
KeywordsNormal Subgroup Compact Group Unitary Representation Closed Subgroup Regular Representation
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