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...

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Detalles Bibliográficos
Autores: Calabuig, J. M., Delgado Garrido, Olvido, Sánchez Pérez, E. A.
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
Descripción
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.