Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the von Neumann algebra of an ergodic group action

Author: Robert J. Zimmer
Journal: Proc. Amer. Math. Soc. 66 (1977), 289-293
MSC: Primary 28A65
MathSciNet review: 0460599
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] J. Dixmier, Les algèbres d'opérateurs dans l'espace Hilbertien, Gauthier-Villars, Paris, 1969.
  • [2] R. E. Edwards, Functional analysis, Holt, Rinehart and Winston, New York, 1965. MR 0221256 (36:4308)
  • [3] F. P. Greenleaf, Amenable actions of locally compact groups, J. Functional Anal. 4 (1969), 295-315. MR 0246999 (40:268)
  • [4] G. W. Mackey, Ergodic theory and virtual groups, Math. Ann. 166 (1966), 187-207. MR 0201562 (34:1444)
  • [5] S. Sakai, $ {C^\ast}$-algebras and $ {W^\ast}$-algebras, Springer-Verlag, New York, 1971. MR 0442701 (56:1082)
  • [6] J. T. Schwartz, $ {W^\ast}$-algebras, Gordon and Breach, New York, 1967. MR 0232221 (38:547)
  • [7] R. J. Zimmer, Amenable ergodic group actions and an application to Poisson boundaries of random walks, J. Functional Analysis (to appear). MR 0473096 (57:12775)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A65

Retrieve articles in all journals with MSC: 28A65

Additional Information

Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society