Ideal-Triangularizability of Semigroups of Positive Operators

Abstract.

Let ${\mathcal{S}}$ be a multiplicative semigroup of positive operators on a Banach lattice E such that every $S \in {\mathcal{S}}$ is ideal-triangularizable, i.e., there is a maximal chain of closed subspaces of E that consists of closed ideals invariant under S. We consider the question under which conditions the whole semigroup ${\mathcal{S}}$ is simultaneously ideal-triangularizable. In particular, we extend a recent result of G. MacDonald and H. Radjavi. We also introduce a class of positive operators that contains all positive abstract integral operators when E is Dedekind complete.