Forum of Mathematics, Sigma

  • Forum of Mathematics, Sigma / Volume 2 / 2014, e2 (12 pages)
  • © 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/>.
  • DOI: http://dx.doi.org/10.1017/fms.2013.6 (About DOI), Published online: 10 March 2014
  • OPEN ACCESS

A NONSEPARABLE AMENABLE OPERATOR ALGEBRA WHICH IS NOT ISOMORPHIC TO A -ALGEBRA

YEMON CHOIa1, ILIJAS FARAHa2a3 and NARUTAKA OZAWAa4

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; narutaka@kurims.kyoto-u.ac.jp

Abstract

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:

  • 47L30;
  • (primary); 46L05;
  • 03E75 (secondary)
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