Compact and weakly compact Lipschitz operators

Any Lipschitz map $f : M \to N$ between two pointed metric spaces may be extended in a unique way to bounded linear operator $\widehat {f} \mathcal {F}(M) {F}(N)$ their corresponding Lipschitz-free spaces. In this paper, we give necessary and sufficient condition for {f}$ compact terms of conditions on $f$ . This extends result by A. Jiménez-Vargas M. Villegas-Vallecillos the case non-separable unbounded After studying behaviour weakly convergent sequences made finitely supported elements spaces, also deduce that is if only it compact.