On the amenability of partial and enveloping actions
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- by Fernando Abadie and Laura Martí Pérez PDF
- Proc. Amer. Math. Soc. 137 (2009), 3689-3693 Request permission
Abstract:
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.References
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Additional Information
- Fernando Abadie
- Affiliation: Centro de Matemática, Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400, Montevideo, Uruguay
- Email: fabadie@cmat.edu.uy
- Laura Martí Pérez
- Affiliation: Centro de Matemática, Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400, Montevideo, Uruguay – and – Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
- Email: lau@cmat.edu.uy, lrmarti@uwaterloo.ca
- Received by editor(s): December 10, 2007
- Published electronically: June 11, 2009
- Communicated by: Marius Junge
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 3689-3693
- MSC (2000): Primary 46L55
- DOI: https://doi.org/10.1090/S0002-9939-09-09998-5
- MathSciNet review: 2529875