NON-UNITARIZABLE GROUPS

Abstract

A group $G$ is called unitarizable, if every uniformly bounded representation $\pi:G \rightarrow B(H)$ 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 $n_1\geq 665$ . 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.