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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1209424-3
PII: S 0002-9939(1994)1209424-3
Keywords: Amenable actions, weak containment of representations
Article copyright: © Copyright 1994 American Mathematical Society