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arXiv · 0902.4585

The Dixmier problem, lamplighters and Burnside groups

Nicolas Monod·Narutaka Ozawa
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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.

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Nicolas Monod, Narutaka Ozawa. 2009-02-26. The Dixmier problem, lamplighters and Burnside groups. https://doi.org/10.1016/j.jfa.2009.06.029

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