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

Published online by Cambridge University Press:  02 June 2020

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])

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.

Type
Original Article
Copyright
© The Author(s) 2020. Published by Cambridge University Press

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