[Return to main list of publications]## A nonseparable amenable operator algebra which is not isomorphic to a C*-algebra

#### Authors

Yemon Choi, Ilijas Farah, Narutaka Ozawa^{*}

* *Corresponding author*

#### Metadata

MSC 2010: 47L30 (primary); 03E75 46L05 (secondary)

DOI: 10.1017/fms.2013.6

#### Status

Appeared as
Forum of Mathematics, Sigma, **2** (2014), e2 (12 pages)

Preprint version available at arXiv 1309.2145

#### Reviews

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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.

#### Updates/comments

The original preprint of this paper was written by IF and NO, with the original counterexample containing all of $K(H)$ and hence not being contained in a subhomogeneous von Neumann algebra. YC's contributions, among them the observation that the original method could be adapted to get counterexamples inside $\ell^\infty\overline{\otimes}{\bf M}_2$, came in later versions.

Yemon Choi