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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the amenability of partial and enveloping actions


Authors: Fernando Abadie and Laura Martí Pérez
Journal: Proc. Amer. Math. Soc. 137 (2009), 3689-3693
MSC (2000): Primary 46L55
Published electronically: June 11, 2009
MathSciNet review: 2529875
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09998-5
PII: S 0002-9939(09)09998-5
Received by editor(s): December 10, 2007
Published electronically: June 11, 2009
Communicated by: Marius Junge
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.