Joint local quasinilpotence and common invariant subspaces

Abstract

In this article we obtain some positive results about the existence of a common nontrivial invariant subspace forN-tuples of not necessarily commuting operators on Banach spaces with a Schauder basis. The concept of joint quasinilpotence plays a basic role. Our results complement recent work by Kosiek [6] and Ptak [8].