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Residual finite dimensionality and representations of amenable operator algebras

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trprfd20181019_JMAAresub.pdf (546.1 KB)

Date

2019-04-15

Authors

Clouâtre, Raphaël
Marcoux, Laurent W.

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

Abstract

We consider a version of a famous open problem formulated by Kadison, asking whether bounded representations of operator algebras are automatically completely bounded. We investigate this question in the context of amenable operator algebras, and we provide an affirmative answer for representations whose range is residually finite-dimensional. Furthermore, we show that weak-⁎ closed, amenable, residually finite-dimensional operator algebras are similar to ⁎-algebras, and in particular have the property that all their bounded representations are completely bounded. We prove our results for operator algebras having the so-called total reduction property, which is known to be weaker than amenability.

Description

The final publication is available at Elsevier via https://doi.org/10.1016/j.jmaa.2018.11.079. © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

Kadison's conjecture, amenable operator algebras, completely bounded maps

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Citation

URI

https://doi.org/10.1016/j.jmaa.2018.11.079
 http://hdl.handle.net/10012/15733

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Waterloo Research
Pure Mathematics