Non-unitarizable groups

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.