The approximation property for spaces of Lipschitz functions

TL;DR

This paper characterizes the approximation property of Lipschitz function spaces on metric spaces using tensor products, the epsilon-product, and linearization techniques, providing new insights into their functional-analytic structure.

Contribution

It introduces a characterization of the approximation property for Lipschitz function spaces with the bounded weak* topology, employing advanced tensor and linearization methods.

Findings

Provides a new characterization of the approximation property for Lipschitz spaces

Utilizes tensor product and epsilon-product techniques in the analysis

Connects Lipschitz function spaces with linearization and topological tensor products

Abstract

Let $\mathrm{Lip}_0(X)$ be the space of all Lipschitz scalar-valued functions on a pointed metric space $X$. We characterize the approximation property for $\mathrm{Lip}_0(X)$ with the bounded weak* topology using as tools the tensor product, the $\epsilon$-product and the linearization of Lipschitz mappings.