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On the amenability of partial and enveloping actions
Author(s):
Fernando
Abadie;
Laura
Martí
Pérez
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3689-3693.
MSC (2000):
Primary 46L55
Posted:
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.
References:
-
- 1.
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- 2.
- Fernando Abadie, Applications of ternary rings to
 -algebras and locally  -algebras, preprint, 2007. - 3.
- Ruy Exel, Amenability for Fell bundles, J. Reine Angew. Math. 492 (1997), 41-73. MR 1488064 (99a:46131)
- 4.
- Ruy Exel, Chi-Keung Ng, Approximation property of
 -algebraic bundles, Math. Proc. Cambridge Philos. Soc. 132 (2002), no. 3, 509-522. MR 1891686 (2002k:46189) - 5.
- J. M. Fell, R. S. Doran, Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles, Pure and Applied Mathematics, vol. 126, Academic Press, 1988. MR 0936629 (90c:46002)
- 6.
- Laura Martí, Condiciones de promediabilidad en fibrados de Fell, Master's Thesis, Universidad de la República, Montevideo, Uruguay, 2006.
- 7.
- G. Zeller-Meier, Produits croisés d'une
 -algèbre par un groupe d'automorphismes, J. Math. Pures et Appl., IX Sér., 47 (1968), 101-239. MR 0241994 (39:3329) - 8.
- H. H. Zettl, A characterization of ternary rings of operators, Advances in Math. 48 (1983), 117-143. MR 700979 (84h:46093)
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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:
10.1090/S0002-9939-09-09998-5
PII:
S 0002-9939(09)09998-5
Received by editor(s):
December 10, 2007
Posted:
June 11, 2009
Communicated by:
Marius Junge
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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