We consider a countable discrete group Γ acting ergodically on a standard Borel space S with quasi-invariant measure μ. Let π be a unitary representation of “nicely” related with S. We prove that if Γ acts amenably on S then π is weakly contained in the regular representation
Kuhn, M. (1994). Amenable actions and weak containment of certain representations of discrete groups. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 122(3), 751-757 [10.1090/S0002-9939-1994-1209424-3].
Amenable actions and weak containment of certain representations of discrete groups
KUHN, MARIA GABRIELLA
1994
Abstract
We consider a countable discrete group Γ acting ergodically on a standard Borel space S with quasi-invariant measure μ. Let π be a unitary representation of “nicely” related with S. We prove that if Γ acts amenably on S then π is weakly contained in the regular representation
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