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

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

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: [email protected])
PAUL JOLISSAINT
Affiliation:
Université de Neuchâtel, Institut de Mathématiques, E.-Argand 11, 2000 Neuchâtel, Switzerland (e-mail: [email protected], [email protected])
ALEXANDRE ZUMBRUNNEN
Affiliation:
Université de Neuchâtel, Institut de Mathématiques, E.-Argand 11, 2000 Neuchâtel, Switzerland (e-mail: [email protected], [email protected])
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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

Adams, S., Elliot, G. A. and Giordano, T.. Amenable actions of groups. Trans. Amer. Math. Soc. 344 (1994), 803–822.Google Scholar
Bekka, B., de la Harpe, P. and Valette, A.. Kazhdan’s Property (T). Cambridge University Press, Cambridge, 2008.Google Scholar
Billingsley, P.. Probability and Measure. John Wiley, New York, 1979.Google Scholar
Chatterji, I., Drutu, C. and Haglund, F.. Kazhdan and Haagerup properties from the median viewpoint. Adv. Math. 225 (2010), 882–921.Google Scholar
Cherix, P.-A., Cowling, M., Jolissaint, P., Julg, P. and Valette, A.. Groups with the Haagerup Property (Gromov’s a-T-Menability). Birkhäuser, Basel, 2001.Google Scholar