Compact ideals and rigidity of representations for amenable operator algebras
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Date
2019
Authors
Clouâtre, Raphaël
Marcoux, Laurent W.
Journal Title
Journal ISSN
Volume Title
Publisher
Polish Academy of Sciences
Abstract
We examine rigidity phenomena for representations of amenable operator algebras which have an ideal of compact operators. We establish that a generalized version of Kadison’s conjecture on completely bounded homomorphisms holds for the algebra if the associated quotient is abelian. We also prove that injective completely bounded representations of the algebra are similar to complete isometries. The main motivating example for these investigations is the recent construction by Choi, Farah and Ozawa of an amenable operator algebra that is not similar to a C∗-algebra, and we show how it fits into our framework. All of our results hold in the presence of the total reduction property, a property weaker than amenability.
Description
Version of record available at https://doi.org/10.4064/sm170328-12-10
Keywords
amenable operator algebras