Approximation properties and Schauder decompositions in Lipschitz-free spaces

TL;DR

This paper demonstrates that Lipschitz-free spaces over doubling metric spaces have the bounded approximation property and that those over ^N or  have monotone finite-dimensional Schauder decompositions, advancing understanding of their structure.

Contribution

It establishes the bounded approximation property for Lipschitz-free spaces over doubling metric spaces and constructs monotone Schauder decompositions for spaces over ^N and .

Findings

Lipschitz-free spaces over doubling metric spaces have the bounded approximation property.

Lipschitz-free spaces over ^N and  have monotone finite-dimensional Schauder decompositions.

Abstract

We prove that the Lipschitz-free space over a doubling metric space has the bounded approximation property. We also show that the Lipschitz-free spaces over $\ell_1^N$ or $\ell_1$ have monotone finite-dimensional Schauder decompositions.