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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
MathSciNet review: 0473849
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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)

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Keywords: $ {C^ \ast }$-algebra, discrete group, inner amenable
Article copyright: © Copyright 1978 American Mathematical Society

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