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Amenable actions and weak containment of certain representations of discrete groups

Author: M. Gabriella Kuhn
Journal: Proc. Amer. Math. Soc. 122 (1994), 751-757
MSC: Primary 43A07; Secondary 22D10
MathSciNet review: 1209424
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Abstract: We consider a countable discrete group $ \Gamma $ acting ergodically on a standard Borel space S with quasi-invariant measure $ \mu $. Let $ \pi $ be a unitary representation of $ \Gamma $ on $ {L^2}(S,d\mu ,\mathcal{H})$ "nicely" related with S. We prove that if $ \Gamma $ acts amenably on S then $ \pi $ is weakly contained in the regular representation.

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Keywords: Amenable actions, weak containment of representations
Article copyright: © Copyright 1994 American Mathematical Society

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