Authors: Ufnarovskij V. A.
Abstract
Let $C = AB-BA$ be a matrix of rang 1. Three different proofs, that $A$ and $B$ has nontrivial common invariant subspace are suggested. The last proof is based on the more general result: if $a$ and $b$ are generators of
an associative algebra $A$ over field $K$ of zero characteristic and for $c=[a,b]$ we have $c(Ac\cap [A,A]) = 0$, then $Ac \subseteq [A,A]$.
Institutul de Matematica Academia de Ştiinţe a Moldovei
str. Academiei 5, Chişinău MD-2028, Moldova