Factorization of weakly compact operators between Banach spaces and Fréchet or (LB)-spaces
[EN] In this note we show that weakly compact operators from a Banach space X into a complete (LB)-space E need not factorize through a reflexive Banach space. If E is a Fréchet space, then weakly compact operators from a Banach space X into E factorize through a reflexive Banach space. The factoriz...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/58753 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/58753 |
| Access Level: | acceso abierto |
| Palabra clave: | Weakly compact operators Reflexive operators Factorization Reflexive Banach spaces (LB)-spaces Fréchet spaces MATEMATICA APLICADA |
| Sumario: | [EN] In this note we show that weakly compact operators from a Banach space X into a complete (LB)-space E need not factorize through a reflexive Banach space. If E is a Fréchet space, then weakly compact operators from a Banach space X into E factorize through a reflexive Banach space. The factorization of operators from a Fréchet or a complete (LB)-space into a Banach space mapping bounded sets into relatively weakly compact sets is also investigated. |
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