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Invariant subspaces of positive strictly singular operators on Banach lattices |
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| Authors: | Julio Flores |
| Institution: | a Department of Applied Mathematics, Escet, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain b Department of Mathematical Analysis, Universidad Complutense de Madrid, 28040 Madrid, Spain c Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada |
| Abstract: | It is shown that every positive strictly singular operator T on a Banach lattice satisfying certain conditions is AM-compact and has invariant subspaces. Moreover, every positive operator commuting with T has an invariant subspace. It is also proved that on such spaces the product of a disjointly strictly singular and a regular AM-compact operator is strictly singular. Finally, we prove that on these spaces the known invariant subspace results for compact-friendly operators can be extended to strictly singular-friendly operators. |
| Keywords: | Strictly singular operator Disjointly strictly singular operator Positive operator AM-compact operator Dunford-Pettis operator Banach lattice Invariant subspace Invariant ideal |
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