Infinite dimensional spaces in the set of strongly norm-attaining Lipschitz maps

TL;DR

This paper proves that for any infinite complete metric space, the set of strongly norm-attaining Lipschitz functions contains a subspace isomorphic to c_0, resolving an open question in the field.

Contribution

It establishes the existence of a c_0 subspace within the set of strongly norm-attaining Lipschitz functions on infinite metric spaces, answering a previously open problem.

Findings

The set of strongly norm-attaining Lipschitz functions contains a c_0 subspace.

This result applies to all infinite complete metric spaces.

It resolves an open question by Kadets and Roldán.

Abstract

We prove that if $M$ is an infinite complete metric space then the set of strongly norm-attaining Lipschitz functions $\SA(M)$ contains a linear subspace isomorphic to $c_0$. This solves an open question posed by V. Kadets and O. Rold\'an.