On the amenability of partial and enveloping actions

On the amenability of partial and enveloping actions

We prove that a partial action is amenable if and only if so is its Morita enveloping action. As applications we prove that any partial representation of a discrete group is positive definite, and we extend a result of Zeller-Meier concerning the amenability of discrete groups and the existence of i...

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Hauptverfasser: Abadie, Fernando, Pérez, Laura Martí
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Operator Algebras
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Zusammenfassung:We prove that a partial action is amenable if and only if so is its Morita enveloping action. As applications we prove that any partial representation of a discrete group is positive definite, and we extend a result of Zeller-Meier concerning the amenability of discrete groups and the existence of invariant states to partial actions.
DOI:10.48550/arxiv.0906.1562