Amenable actions and weak containment of certain representations of discrete groups

Kuhn, M. Gabriella

doi:10.1090/S0002-9939-1994-1209424-3

Amenable actions and weak containment of certain representations of discrete groups
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by M. Gabriella Kuhn PDF

Proc. Amer. Math. Soc. 122 (1994), 751-757 Request permission

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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Ergodic theory and semisimple groups