On the ideal-triangularizability of positive operators on Banach lattices |
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Authors: | Mohammed Taghi Jahandideh |
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Institution: | Department of Mathematics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5 |
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Abstract: | There are some known results that guarantee the existence of a nontrivial closed invariant ideal for a quasinilpotent positive operator on an -space with unit or a Banach lattice whose positive cone contains an extreme ray. Some recent results also guarantee the existence of such ideals for certain positive operators, e.g. a compact quasinilpotent positive operator, on an arbitrary Banach lattice. The main object of this article is to use these results in constructing a maximal closed ideal chain, each of whose members is invariant under a certain collection of operators that are related to compact positive operators, or to quasinilpotent positive operators. |
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