Commutators of small rank and reducibility of operator semigroups

Ali Jafarian, Alexey I. Popov, Mehdi Radjabalipour +1

It is easy to see that if $\cG$ is a non-abelian group of unitary matrices, then for no members $A$ and $B$ of $\cG$ can the rank of $AB-BA$ be one. We examine the consequences of…