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- W2276835986 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 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." @default.
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- W2276835986 date "2016-04-01" @default.
- W2276835986 modified "2023-09-27" @default.
- W2276835986 title "Optimal extensions of compactness properties for operators on Banach function spaces" @default.
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- W2276835986 doi "https://doi.org/10.1016/j.topol.2015.12.075" @default.
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