The Dixmier problem, lamplighters and Burnside groups

J.Dixmier asked in 1950 whether every non-amenable group admits uniformly bounded representations that cannot be unitarised. We provide such representations upon passing to extensions by abelian groups. This gives a new characterisation of amenability. Furthermore, we deduce that certain Burnside groups are non-unitarisable, answering a question raised by G. Pisier.


Published in:
Journal of Functional Analysis, 258, 1, 255--259
Year:
2010
ISSN:
0022-1236
Keywords:
Laboratories:




 Record created 2009-02-25, last modified 2018-03-17


Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)