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)

 
 

 

Inner amenability and fullness


Author: Marie Choda
Journal: Proc. Amer. Math. Soc. 86 (1982), 663-666
MSC: Primary 46L35
DOI: https://doi.org/10.1090/S0002-9939-1982-0674101-6
MathSciNet review: 674101
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be a countable group which is not inner amenable. Then the II$ _{1}$-factor $ M$ is full in the following cases:

(1) $ M$ is given by the group measure space construction from a triple $ (X,\mu ,G)$ with respect to a strongly ergodic measure preserving action of $ G$ on a probability space $ (X,\mu )$.

(2) $ M$ is the crossed product of a full II$ _{1}$-factor by $ G$ with respect to an action.


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

  • [1] C. A. Akemann and M. Walter, Unbounded negative definite functions, Canad. J. Math. 33 (1981), 862-871. MR 634144 (83b:43009)
  • [2] M. Choda and Y. Watatani, Fixed point algebra and property T, Math. Japon. 27 (1982), 263-266. MR 655229 (83i:46065)
  • [3] M. Choda, Property $ {\text{T}}$ and fullness of the group measure space construction, Math. Japon. 27 (1982), 535-539. MR 667819 (83j:46073)
  • [4] A. Connes, Almost periodic states and factors of type III$ _{1}$, J. Funct. Anal. 16 (1974), 415-445. MR 0358374 (50:10840)
  • [5] A. Connes and B. Weiss, Property $ {\text{T}}$ and asymptotically invariant sequences, Israel J. Math. 37 (1980), 209-210. MR 599455 (82e:28023b)
  • [6] E. G. Effros, Property $ \Gamma $ and inner amenability, Proc. Amer. Math. Soc. 47 (1975), 483-486. MR 0355626 (50:8100)
  • [7] Y. Haga and Z. Takeda, Correspondence between subgroups and subalgebras in a cross product von Neumann algebra, Tôhoku Math. J. 21 (1972), 167-190. MR 0380439 (52:1339)
  • [8] D. A. Kazhdan, Connection of the dual space of a group with the structure of its closed subgroups, Funct. Anal. Appl. 1 (1967), 63-65. MR 0209390 (35:288)
  • [9] F. Murray and J. von Neumann, On rings of operators. IV, Ann. of Math. 44 (1943), 716-808. MR 0009096 (5:101a)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L35

Retrieve articles in all journals with MSC: 46L35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0674101-6
Keywords: Factor, group algebra, crossed product, ergodicity
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society