Generalized perfect spaces
Given two Banach function spaces X and Y related to a measure μ, the Y-dual space XY of X is defined as the space of the multipliers from X to Y. The space XY is a generalization of the classical Köthe dual space of X, which is obtained by taking Y = Lt(μ). Under minimal conditions, we can consider...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2008 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/103459 |
| Acceso en línea: | https://hdl.handle.net/11441/103459 https://doi.org/10.1016/S0019-3577(09)00008-1 |
| Access Level: | acceso abierto |
| Palabra clave: | Banach function spaces Köthe dual Perfect spaces Fatou property p-Convexity p-Concavity |
| Sumario: | Given two Banach function spaces X and Y related to a measure μ, the Y-dual space XY of X is defined as the space of the multipliers from X to Y. The space XY is a generalization of the classical Köthe dual space of X, which is obtained by taking Y = Lt(μ). Under minimal conditions, we can consider the Y-bidual space XYY of X (i.e. the Y-dual of XY). As in the classical case, the containment X ⊂ XYY always holds. We give conditions guaranteeing that X coincides with XYY, in which case X is said to be Y-perfect. We also study when X is isometrically embedded in XYY. Properties involving p-convexity, p-concavity and the order of X and Y, will have a special relevance. |
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