On Lipschitz-free spaces over spheres of Banach spaces

TL;DR

This paper proves that for Banach spaces isomorphic to their hyperplanes, the Lipschitz-free spaces over the space and its sphere are structurally equivalent.

Contribution

It establishes an isomorphism between Lipschitz-free spaces over certain Banach spaces and their spheres, extending understanding of their geometric properties.

Findings

Lipschitz-free spaces over Banach spaces isomorphic to their hyperplanes are isomorphic to those over their spheres.

The result applies to a broad class of Banach spaces with this hyperplane property.

Provides new insights into the structure of Lipschitz-free spaces in geometric functional analysis.

Abstract

We prove that, for each Banach space $X$ which is isomorphic to its hyperplanes, the Lipschitz-free spaces over $X$ and over its sphere are isomorphic.