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• W3204571867 abstract "Any Lipschitz map $f : M to N$ between two pointed metric spaces may be extended in a unique way to a bounded linear operator $widehat {f} : mathcal {F}(M) to mathcal {F}(N)$ between their corresponding Lipschitz-free spaces. In this paper, we give a necessary and sufficient condition for $widehat {f}$ to be compact in terms of metric conditions on $f$ . This extends a result by A. Jiménez-Vargas and M. Villegas-Vallecillos in the case of non-separable and unbounded metric spaces. After studying the behaviour of weakly convergent sequences made of finitely supported elements in Lipschitz-free spaces, we also deduce that $widehat {f}$ is compact if and only if it is weakly compact." @default.
• W3204571867 created "2021-10-11" @default.
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• W3204571867 date "2022-05-11" @default.
• W3204571867 modified "2023-09-24" @default.
• W3204571867 title "Compact and weakly compact Lipschitz operators" @default.
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• W3204571867 doi "https://doi.org/10.1017/prm.2022.29" @default.
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