COMMON INVARIANT SUBSPACES FOR N-TUPLES OF POSITIVE OPERATORS ACTING ON TOPOLOGICAL VECTOR SPACES

Abstract

Let $(T_1,\dots,T_N)$ be a $N-$tuple of positive operators with respect a Markushevich basis which are defined on a Hausdorff topological vector space. In this work we extend the notion of weak local quasinilpotence to $N-$tuples of operators (not-necessarily commuting). Under the hypothesis of existence of positive vectors, joint weak locally quasinilpotent we will obtain the existence of common invariant subspaces.