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Respresentations of strongly amenable $ C\sp{\ast} $-algebras

Author: John Bunce
Journal: Proc. Amer. Math. Soc. 32 (1972), 241-246
MSC: Primary 46L05
MathSciNet review: 0295091
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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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Keywords: Amenable groups, strongly amenable $ {C^\ast}$-algebras, hyperfinite $ {C^\ast}$-algebras, GCR algebras, representations, invariant operator range
Article copyright: © Copyright 1972 American Mathematical Society