The Dixmier problem, lamplighters and Burnside groups
Group Theory
2010-01-17 v1 Functional Analysis
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.
Cite
@article{arxiv.0902.4585,
title = {The Dixmier problem, lamplighters and Burnside groups},
author = {Nicolas Monod and Narutaka Ozawa},
journal= {arXiv preprint arXiv:0902.4585},
year = {2010}
}
Comments
4 pages