Vector measures: where are their integrals?
Let ν be a vector measure with values in a Banach space Z. The integration map Iν:L1(ν)→Z, given by f↦∫fdν for f ∈ L 1(ν), always has a formal extension to its bidual operator I∗∗ν:L1(ν)∗∗→Z∗∗. So, we may consider the “integral” of any element f ** of L 1(ν)** as I **ν(f **). Our aim is to identify...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/103784 |
| Acceso en línea: | https://hdl.handle.net/11441/103784 https://doi.org/10.1007/s11117-008-2191-1 |
| Access Level: | acceso abierto |
| Palabra clave: | Banach lattices and function spaces Vector measure Integration map Duality |
| Sumario: | Let ν be a vector measure with values in a Banach space Z. The integration map Iν:L1(ν)→Z, given by f↦∫fdν for f ∈ L 1(ν), always has a formal extension to its bidual operator I∗∗ν:L1(ν)∗∗→Z∗∗. So, we may consider the “integral” of any element f ** of L 1(ν)** as I **ν(f **). Our aim is to identify when these integrals lie in more tractable subspaces Y of Z **. For Z a Banach function space X, we consider this question when Y is any one of the subspaces of X ** given by the corresponding identifications of X, X′′ (the Köthe bidual of X) and X′* (the topological dual of the Köthe dual of X). Also, we consider certain kernel operators T and study the extended operator I **ν for the particular vector measure ν defined by ν(A) := T(χ A ). |
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