A note on attaining diameter two properties in Lipschitz-free spaces

TL;DR

This paper demonstrates that in Lipschitz-free spaces, various diameter two properties are equivalent to their attaining variants, clarifying their relationships.

Contribution

It establishes the equivalence between diameter two properties and their attaining variants in Lipschitz-free spaces.

Findings

Diameter two properties coincide with their attaining variants in Lipschitz-free spaces.

The strong diameter two property, the diameter two property, and the local diameter two property are equivalent to their attaining counterparts.

Abstract

We prove that in Lipschitz-free spaces the strong diameter two property, the diameter two property, and the local diameter two property coincide with their corresponding attaining variants.