English

On the weak$^*$ separability of the space of Lipschitz functions

Functional Analysis 2025-03-14 v1

Abstract

We conjecture that whenever MM is a metric space of density at most continuum, then the space of Lipschitz functions is ww^*-separable. We prove the conjecture for several classes of metric spaces including all the Banach spaces with a projectional skeleton, Banach spaces with a ww^*-separable dual unit ball and locally separable complete metric spaces.

Keywords

Cite

@article{arxiv.2406.03982,
  title  = {On the weak$^*$ separability of the space of Lipschitz functions},
  author = {Leandro Candido and Marek Cuth and Benjamin Vejnar},
  journal= {arXiv preprint arXiv:2406.03982},
  year   = {2025}
}