TY - JOUR

T1 - A nonseparable amenable operator algebra which is not isomorphic to a {$C^*$}-algebra

AU - Choi, Yemon

AU - Farah, Ilijas

AU - Ozawa, Narutaka

N1 - © 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.

PY - 2014/3/10

Y1 - 2014/3/10

N2 - 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.

AB - 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.

U2 - 10.1017/fms.2013.6

DO - 10.1017/fms.2013.6

M3 - Journal article

VL - 2

JO - Forum of Mathematics, Sigma

JF - Forum of Mathematics, Sigma

SN - 2050-5094

M1 - e2

ER -