Monod, NicolasOzawa, Narutaka2009-02-252009-02-252009-02-25201010.1016/j.jfa.2009.06.029https://infoscience.epfl.ch/handle/20.500.14299/35651WOS:000271729100011J.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.Unitarisable representationAmenable groupBurnside grouptext::journal::journal article::research article