Respresentations of strongly amenable $C^{\ast }$-algebras
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- 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.References
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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