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 conjugation operators


Author: William L. Paschke
Journal: Proc. Amer. Math. Soc. 71 (1978), 117-118
MSC: Primary 46L05; Secondary 22D25
DOI: https://doi.org/10.1090/S0002-9939-1978-0473849-5
MathSciNet review: 0473849
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that an infinite discrete group G is inner amenable if and only if the $ {C^ \ast }$-algebra generated by the unitaries on $ {l^2}(G)$ corresponding to conjugation by s $ (s \in G)$ does not contain the projection on the point-mass at the identity.


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

  • [1] C. A. Akemann and P. A. Ostrand, Computing norms in group $ {C^\ast}$-algebras, Amer. J. Math. 98 (1976), 1015-1047. MR 0442698 (56:1079)
  • [2] -, On a tensor product $ {C^\ast}$-algebra associated with the free group on two generators (preprint).
  • [3] E. G. Effros, Property $ \Gamma $ and inner amenability, Proc. Amer. Math. Soc. 47 (1975), 483-486. MR 0355626 (50:8100)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L05, 22D25

Retrieve articles in all journals with MSC: 46L05, 22D25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0473849-5
Keywords: $ {C^ \ast }$-algebra, discrete group, inner amenable
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society