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Compact ideals and rigidity of representations for amenable operator algebras

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dc.contributor.authorClouâtre, Raphaël
dc.contributor.authorMarcoux, Laurent W.
dc.date.accessioned2020-04-02T17:47:49Z
dc.date.available2020-04-02T17:47:49Z
dc.date.issued2019
dc.descriptionVersion of record available at https://doi.org/10.4064/sm170328-12-10en
dc.description.abstractWe 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.en
dc.description.sponsorshipThe first author was partially supported by an FQRNT postdoctoral fellowship and an NSERC Discovery Grant. The second author was partially supported by an NSERC Discovery Grant.en
dc.identifier.urihttps://doi.org/10.4064/sm170328-12-10
dc.identifier.urihttp://hdl.handle.net/10012/15734
dc.language.isoenen
dc.publisherPolish Academy of Sciencesen
dc.subjectamenable operator algebrasen
dc.titleCompact ideals and rigidity of representations for amenable operator algebrasen
dc.typeArticleen
dcterms.bibliographicCitationClouâtre, Raphaël, and Laurent W. Marcoux. “Compact Ideals and Rigidity of Representations for Amenable Operator Algebras.” Studia Mathematica 244 (2019): 25–41. https://doi.org/10.4064/sm170328-12-10.en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Pure Mathematicsen
uws.peerReviewStatusRevieweden
uws.scholarLevelFacultyen
uws.typeOfResourceTexten

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