Invariant subspaces for positive operators on Banach spaces with unconditional basis
We prove that every lattice homomorphism acting on a Banach space X with the lattice structure given by an unconditional basis has a non-trivial closed invariant subspace. In fact, it has a non-trivial closed invariant ideal, which is no longer true for every positive operator on such a space. Motiv...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/71793 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/71793 |
| Access Level: | acceso abierto |
| Palabra clave: | 517.982.22 Banach lattices Lattice homomorphisms Invariant subspaces Invariant ideals Análisis funcional y teoría de operadores |
| Sumario: | We prove that every lattice homomorphism acting on a Banach space X with the lattice structure given by an unconditional basis has a non-trivial closed invariant subspace. In fact, it has a non-trivial closed invariant ideal, which is no longer true for every positive operator on such a space. Motivated by these examples, we characterize tridiagonal positive operators without non-trivial closed invariant ideals on X extending to this context a result of Grivaux on the existence of non-trivial closed invariant subspaces for tridiagonal operators. |
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