The Dixmier problem, lamplighters and Burnside groups

Details The Dixmier problem, lamplighters and Burnside groups The Dixmier problem, lamplighters and Burnside groups

2009-02-26

arxiv.org/abs/0902.4585v1

J. of Functional Analysis 258 No. 1 (2010) 255--259

Mathematics

Group Theory

4 pages

Scientific paper

10.1016/j.jfa.2009.06.029

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.

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