Abstract
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.
Details
Title
The Dixmier problem, lamplighters and Burnside groups
Author(s)
Monod, Nicolas ; Ozawa, Narutaka
Published in
Journal of Functional Analysis
Volume
258
Issue
1
Pages
255--259
Date
2010
ISSN
0022-1236
Other identifier(s)
View record in Web of Science
Laboratories
EGG
Record Appears in
Scientific production and competences > SB - School of Basic Sciences > MATH - Institute of Mathematics > EGG - Chair of ergodic and geometric group theory
Scientific production and competences > SB - School of Basic Sciences > Mathematics
Peer-reviewed publications
Work produced at EPFL
Journal Articles
Published
Scientific production and competences > SB - School of Basic Sciences > Mathematics
Peer-reviewed publications
Work produced at EPFL
Journal Articles
Published
Record creation date
2009-02-25