Geodesic
A NONSEPARABLE AMENABLE OPERATOR ALGEBRA WHICH IS NOT ISOMORPHIC TO A $C^*$ -ALGEBRA
Forum of Mathematics, Sigma, Tome 2 (2014)

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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. 
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     author = {YEMON CHOI and ILIJAS FARAH and NARUTAKA OZAWA},
     title = {A {NONSEPARABLE} {AMENABLE} {OPERATOR} {ALGEBRA} {WHICH} {IS} {NOT} {ISOMORPHIC} {TO} {A} $C^*$ {-ALGEBRA}},
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     publisher = {mathdoc},
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     doi = {10.1017/fms.2013.6},
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YEMON CHOI; ILIJAS FARAH; NARUTAKA OZAWA. A NONSEPARABLE AMENABLE OPERATOR ALGEBRA WHICH IS NOT ISOMORPHIC TO A $C^*$ -ALGEBRA. Forum of Mathematics, Sigma, Tome 2 (2014). doi: 10.1017/fms.2013.6

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