a1 Department of Mathematics and Statistics, University of Saskatchewan, McLean Hall, 106 Wiggins Road, Saskatoon, Saskatchewan, Canada S7N 5E6choi@math.usask.ca
a2 Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3ifarah@mathstat.yorku.ca
a3 Matematicki Institut, Kneza Mihaila 35, Belgrade, Serbia
a4 RIMS, Kyoto University, 606-8502 Japan; firstname.lastname@example.org
It has been a long-standing question whether every amenable operator algebra is isomorphic to a (necessarily nuclear)-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 -algebras and show that our method cannot produce a separable counterexample.
(Received September 29 2013)
(Accepted November 28 2013)
2010 Mathematics Subject Classification: