‎In this paper‎, ‎we study weighted composition operators between Lipschitz algebras of complex-valued bounded functions on metric spaces‎, ‎not necessarily compact‎. ‎We give necessary and sufficient conditions for the injectivity and the surjectivity of these operators‎. ‎We also obtain sufficient and necessary conditions for a weighted composition operator between these spaces to be compact.

We study weighted composition operators on Banach spaces over unbounded, locally finite metric spaces. characterize the that are bounded, compact, being bounded below, having closed range, invertible, a (surjective) isometry, and Fredholm. Several examples presented illustrating diversity of such operators.