Pe{\l}czy\'nski space is isomorphic to the Lipschitz free space over a compact set

TL;DR

This paper proves that the Pe{}czy
44ski space is isomorphic to the Lipschitz free space over a compact set, providing a novel example linking infinite-dimensional Banach spaces and free spaces of compact sets.

Contribution

It establishes the first known example of an infinite-dimensional Banach space whose Lipschitz free space is isomorphic to that of a compact set.

Findings

Pe{}czy
44ski space is isomorphic to a Lipschitz free space over a compact set

First example of such an isomorphism involving infinite-dimensional Banach spaces

Links the structure of Pe{}czy
44ski space with free spaces of compact sets

Abstract

We prove the result stated in the title. This provides a first example of an infinite-dimensional Banach space whose Lipschitz free space is isomorphic to the free space of a compact set.