2021/10/07 by Arafat Abbar, Abbar, Arafat, Clément Coine +3 · 1 citation
Computer Science · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · doi:10.48550/arxiv.2110.03231
openalex publication_date 2021/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Any Lipschitz map f : M → N between two pointed metric spaces may be extended in a unique way to a bounded linear operator \widehatf : \mathcal F(M) → \mathcal F(N) between their corresponding Lipschitz-free spaces. In this paper, we give a necessary and sufficient condition for \widehatf 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 behavior of weakly convergent sequences made of finitely supported elements in Lipschitz-free spaces, we also deduce that \widehatf is compact if and only if it is weakly compact.