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Ideal-Triangularizability of Semigroups of Positive Operators

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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.

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Correspondence to Marko Kandić.

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Drnovšek, R., Kandić, M. Ideal-Triangularizability of Semigroups of Positive Operators. Integr. equ. oper. theory 64, 539–552 (2009).

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Mathematics Subject Classification (2000).