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Amenability, Kazhdan's property T, strong ergodicity and invariant means for ergodic group-actions

Published online by Cambridge University Press:  19 September 2008

Klaus Schmidt
Klaus Schmidt*
Affiliation:
Form the Mathematics Institute, University of Warwick, England
*
†Address for correspondence: Dr Klaus Schmidt, Mathematics Institute, University of Warwick, Coventry CV4 7AL, England.
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Abstract

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This paper discusses the relations between the following properties o finite measure preserving ergodic actions of a countable group G: strong ergodicity (i.e. the non-existence of almost invariant sets), uniqueness of G-invariant means on the measure space carrying the group action, and certain cohomological properties. Using these properties one can characterize all actions of amenable groups and of groups with Kazhdan's property T. For groups which fall in between these two definations these notions lead to some interesting examples.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 2 , June 1981 , pp. 223 - 236
Copyright
Copyright © Cambridge University Press 1981

References

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