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.