Optimal extensions of compactness properties for operators on Banach function spaces
[EN] Compactness type properties for operators acting in Banach function spaces are not always preserved when the operator is extended to a bigger space. Moreover, it is known that there exists a maximal (weakly) compact linear extension of a (weakly) compact operator if and only if its maximal cont...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/99863 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/99863 |
| Access Level: | acceso abierto |
| Palavra-chave: | Vector measures Banach function space AM-compact operator Dunford-Pettis operator Narrow operator Optimal domain MATEMATICA APLICADA |
| Resumo: | [EN] Compactness type properties for operators acting in Banach function spaces are not always preserved when the operator is extended to a bigger space. Moreover, it is known that there exists a maximal (weakly) compact linear extension of a (weakly) compact operator if and only if its maximal continuous linear extension to its optimal domain is (weakly) compact. We show that the same happens if we consider AM-compactness for the operator, and we give some partial results regarding Dunford-Pettis operators. Narrow operators-considered as a family defined by a weak compactness type property-are also analyzed from this point of view. Finally, we provide some applications of the fact that an operator from a Banach function space extends to a narrow operator if and only if it is narrow. (C) 2015 Elsevier B.V. All rights reserved. |
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