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arXiv · 1309.2145

A nonseparable amenable operator algebra which is not isomorphic to a C*-algebra

Yemon Choi·Ilijas Farah·Narutaka Ozawa
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Abstract

It has been a longstanding problem whether every amenable operator algebra is isomorphic to a (necessarily nuclear) C*-algebra. In this note, we give a nonseparable counterexample. The existence of a separable counterexample 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.

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Yemon Choi, Ilijas Farah, Narutaka Ozawa. 2013-11-25. A nonseparable amenable operator algebra which is not isomorphic to a C*-algebra. https://doi.org/10.1017/fms.2013.6

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