SIMULTANEOUS TRIANGULARIZABILITY, NEAR COMMUTATIVITY AND ROTAS THEOREM

In this paper we consider simultaneously triangularizable collections of compact operators and show that similarities of any finite subcolle ction can be made arbitrarily close to commuting normal operators. As a consequence, we obtain a variant of a theorem of G.-C. Rota Also, we give some sufficient conditions for simultaneous triangularization of collections of compact operators. Finally, several counterexamples ar e given.