Compactness in L1 of a vector measure
We study compactness and related topological properties in the space L1(m) of a Banach space valued measure m when the natural topologies associated to convergence of vector valued integrals are considered. The resulting topological spaces are shown to be angelic and the relationship of compactness...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2014 |
| 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:10251/52819 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/52819 |
| Access Level: | acceso abierto |
| Palavra-chave: | Vector measure Integration operator Compactness Angelic space Boundary Positive Schur property Completely continuous operator Almost Dunford Pettis operator Strongly weakly compactly generated space MATEMATICA APLICADA |
| Resumo: | We study compactness and related topological properties in the space L1(m) of a Banach space valued measure m when the natural topologies associated to convergence of vector valued integrals are considered. The resulting topological spaces are shown to be angelic and the relationship of compactness and equi-integrability is explored. A natural norming subset of the dual unit ball of L1(m) appears in our discussion and we study when it is a boundary. The (almost) complete continuity of the integration operator is analyzed in relation with the positive Schur property of L1(m). The strong weaklycompact generation of L1(m) is discussed as well. |
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