INVARIANT SUBSPACES FOR POSITIVE OPERATORS ACTING ON A BANACH-SPACE WITH BASIS

Recently we established several invariant subspace theorems for operators acting on an l(p)-space. In this note we extend these results from operators acting on an l(p)-space to operators acting on any Banach space with a (not necessarily unconditional) Schauder basis. For instance, it is shown that if a continuous quasinilpotent operator on a Banach space is positive with respect to the closed cone generated by a basis, then the operator has a nontrivial closed invariant subspace.