Optimal extensions of compactness properties for operators on Banach function spaces
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Other documents of the author: Calabuig, J. M.; Jiménez-Fernández, Eduardo; Juan, M.A.; Sánchez Pérez, Enrique A.
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Title
Optimal extensions of compactness properties for operators on Banach function spacesDate
2015-04Publisher
ElsevierBibliographic citation
CALABUIG, J. M., et al. Optimal extensions of compactness properties for operators on Banach function spaces. Topology and its Applications, 2016.Type
info:eu-repo/semantics/articlePublisher version
http://www.sciencedirect.com/science/article/pii/S0166864115006082Version
info:eu-repo/semantics/submittedVersionSubject
Abstract
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 ... [+]
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. [-]
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Topology and its Applications Volume 203, April 2016Rights
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