On the amenability of partial and enveloping actions
HTML articles powered by AMS MathViewer
- by Fernando Abadie and Laura Martí Pérez
- Proc. Amer. Math. Soc. 137 (2009), 3689-3693
- DOI: https://doi.org/10.1090/S0002-9939-09-09998-5
- Published electronically: June 11, 2009
- PDF | 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
- Fernando Abadie, Enveloping actions and Takai duality for partial actions, J. Funct. Anal. 197 (2003), no. 1, 14–67. MR 1957674, DOI 10.1016/S0022-1236(02)00032-0
- Fernando Abadie, Applications of ternary rings to $C^*$-algebras and locally $C^*$-algebras, preprint, 2007.
- Ruy Exel, Amenability for Fell bundles, J. Reine Angew. Math. 492 (1997), 41–73. MR 1488064, DOI 10.1515/crll.1997.492.41
- Ruy Exel and Chi-Keung Ng, Approximation property of $C^*$-algebraic bundles, Math. Proc. Cambridge Philos. Soc. 132 (2002), no. 3, 509–522. MR 1891686, DOI 10.1017/S0305004101005837
- J. M. G. Fell and R. S. Doran, Representations of $^*$-algebras, locally compact groups, and Banach $^*$-algebraic bundles. Vol. 2, Pure and Applied Mathematics, vol. 126, Academic Press, Inc., Boston, MA, 1988. Banach $^*$-algebraic bundles, induced representations, and the generalized Mackey analysis. MR 936629, DOI 10.1016/S0079-8169(09)60018-0
- Laura Martí, Condiciones de promediabilidad en fibrados de Fell, Master’s Thesis, Universidad de la República, Montevideo, Uruguay, 2006.
- G. Zeller-Meier, Produits croisés d’une $C^{\ast }$-algèbre par un groupe d’automorphismes, J. Math. Pures Appl. (9) 47 (1968), 101–239 (French). MR 241994
- Heinrich Zettl, A characterization of ternary rings of operators, Adv. in Math. 48 (1983), no. 2, 117–143. MR 700979, DOI 10.1016/0001-8708(83)90083-X
Bibliographic 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