Geodesic
Non-unitarizable groups
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2010), pp. 40-43

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A group $G$ is called unitarizable, if every uniformly bounded representation $\pi:G\to B(H)$ of $G$ on a Hilbert space $H$ is unitarizable. N. Monod and N. Ozawa in [6] prove that free Burnside groups $B(m,n)$ are non unitarizable for arbitrary composite odd number $n=n_1n_2$, where $n_\geq665$. We prove that for the same $n$ the groups $B(4,n)$ have continuum many non-isomorphic factor-groups, each one of which is non-unitarizable and uniformly non-amenable.
Keywords: representation of group, unitarizable group, free Burnside group, periodic group. 
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H. R. Rostami. Non-unitarizable groups. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2010), pp. 40-43. http://geodesic.mathdoc.fr/item/UZERU_2010_3_a4/