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A NONSEPARABLE AMENABLE OPERATOR ALGEBRA WHICH IS NOT ISOMORPHIC TO A
$C^*$-ALGEBRA
Published online by Cambridge University Press: 10 March 2014
Abstract
It has been a long-standing question whether every amenable operator algebra is isomorphic to a (necessarily nuclear) $\mathrm{C}^*$-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
$\mathrm{C}^*$-algebras and show that our method cannot produce a separable counterexample.
MSC classification
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- Research Article
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- Creative Commons
- The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence .
- Copyright
- © The Author(s) 2014
References
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