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

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

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...

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Veröffentlicht in:Ergodic theory and dynamical systems 2021-08, Vol.41 (8), p.2349-2368
Hauptverfasser: DELABIE, THIEBOUT, JOLISSAINT, PAUL, ZUMBRUNNEN, ALEXANDRE
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Dynamical systems
Original Article
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Zusammenfassung: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.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2020.45