Simultaneous similarity, bounded generation and amenability
Simultaneous similarity, bounded generation and amenability
We prove that a discrete group $G$ is amenable if and only if it is strongly unitarizable in the following sense: every unitarizable representation $\pi$ on $G$ can be unitarized by an invertible chosen in the von Neumann algebra generated by the range of $\pi$. Analogously, a $C^*$-algebra $A$ is …