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A new characterization of the Haagerup property by actions on infinite measure spaces

Part of: Locally compact groups and their algebras Measure-theoretic ergodic theory

Published online by Cambridge University Press:  02 June 2020

THIEBOUT DELABIE ,
PAUL JOLISSAINT  and
ALEXANDRE ZUMBRUNNEN
THIEBOUT DELABIE
Affiliation:
Université Paris-Sud, Faculté des Sciences d’Orsay, Département de Mathématiques, Bâtiment 307, F-91405 Orsay Cedex, France (e-mail: thiebout.delabie@gmail.com)
PAUL JOLISSAINT
Affiliation:
Université de Neuchâtel, Institut de Mathématiques, E.-Argand 11, 2000 Neuchâtel, Switzerland (e-mail: paul.jolissaint@unine.ch, alexandre.zumbrunnen@unine.ch)
ALEXANDRE ZUMBRUNNEN
Affiliation:
Université de Neuchâtel, Institut de Mathématiques, E.-Argand 11, 2000 Neuchâtel, Switzerland (e-mail: paul.jolissaint@unine.ch, alexandre.zumbrunnen@unine.ch)
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Abstract

The aim of the article is to provide a characterization of the Haagerup property for locally compact, second countable groups in terms of actions on $\unicode[STIX]{x1D70E}$-finite measure spaces. It is inspired by the very first definition of amenability, namely the existence of an invariant mean on the algebra of essentially bounded, measurable functions on the group.

Keywords

locally compact groupsunitary representationsHaagerup property

MSC classification

Primary: 22D10: Unitary representations of locally compact groups 22D40: Ergodic theory on groups
Secondary: 28D05: Measure-preserving transformations
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 8 , August 2021 , pp. 2349 - 2368
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Copyright
© The Author(s) 2020. Published by Cambridge University Press

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References

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