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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Respresentations of strongly amenable $C^{\ast }$-algebras
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by John Bunce PDF
Proc. Amer. Math. Soc. 32 (1972), 241-246 Request permission

Abstract:

B. E. Johnson has introduced the concept of a strongly amenable ${C^\ast }$-algebra and has proved that GCR algebras and uniformly hyperfinite algebras are strongly amenable. We generalize the well-known Dixmier-Mackey theorem on amenable groups by proving that every continuous representation of a strongly amenable ${C^\ast }$-algebra is similar to a $^\ast$-representation. As an application, we show that every invariant operator range for a Type I von Neumann algebra comes from an operator in the commutant.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 32 (1972), 241-246
  • MSC: Primary 46L05
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0295091-8
  • MathSciNet review: 0295091