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    Rights statement: © The Author(s) 2014 The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence <http://creativecommons.org/licenses/by/3.0/>. http://journals.cambridge.org/action/displayJournal?jid=FMS The final, definitive version of this article has been published in the Journal, Forum of Mathematics, Sigma, 2, e2 2014, © 2014 Cambridge University Press.

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A nonseparable amenable operator algebra which is not isomorphic to a {$C^*$}-algebra

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Article numbere2
<mark>Journal publication date</mark>10/03/2014
<mark>Journal</mark>Forum of Mathematics, Sigma
Volume2
Number of pages12
Publication StatusPublished
<mark>Original language</mark>English

Abstract

It has been a long-standing question whether every amenable operator algebra is isomorphic to a (necessarily nuclear) C*-algebra. In this note, we give a nonseparable counterexample. Finding out whether a separable counterexample exists remains an open problem. We also initiate a general study of unitarizability of representations of amenable groups in C*-algebras and show that our method cannot produce a separable counterexample.

Bibliographic note

© The Author(s) 2014 The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence . http://journals.cambridge.org/action/displayJournal?jid=FMS The final, definitive version of this article has been published in the Journal, Forum of Mathematics, Sigma, 2, e2 2014, © 2014 Cambridge University Press.