On the von Neumann algebra of an ergodic group action
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- by Robert J. Zimmer
- Proc. Amer. Math. Soc. 66 (1977), 289-293
- DOI: https://doi.org/10.1090/S0002-9939-1977-0460599-3
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Abstract:
We give a criterion that an ergodic action be amenable in terms of the operator algebra associated to it by the Murray-von Neumann construction.References
- J. Dixmier, Les algèbres d’opérateurs dans l’espace Hilbertien, Gauthier-Villars, Paris, 1969.
- R. E. Edwards, Functional analysis. Theory and applications, Holt, Rinehart and Winston, New York-Toronto-London, 1965. MR 0221256
- F. P. Greenleaf, Amenable actions of locally compact groups, J. Functional Analysis 4 (1969), 295–315. MR 0246999, DOI 10.1016/0022-1236(69)90016-0
- George W. Mackey, Ergodic theory and virtual groups, Math. Ann. 166 (1966), 187–207. MR 201562, DOI 10.1007/BF01361167
- Shôichirô Sakai, $C^*$-algebras and $W^*$-algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60, Springer-Verlag, New York-Heidelberg, 1971. MR 0442701
- J. T. Schwartz, $W^{\ast }$-algebras, Gordon and Breach Science Publishers, New York-London-Paris, 1967. MR 0232221
- Robert J. Zimmer, Amenable ergodic group actions and an application to Poisson boundaries of random walks, J. Functional Analysis 27 (1978), no. 3, 350–372. MR 0473096, DOI 10.1016/0022-1236(78)90013-7
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 66 (1977), 289-293
- MSC: Primary 28A65
- DOI: https://doi.org/10.1090/S0002-9939-1977-0460599-3
- MathSciNet review: 0460599