On the weak⁎ separability of the space of Lipschitz functions
We conjecture that whenever M is a metric space of density at most continuum, then the space of Lipschitz functions is w ⁎ -separable. We prove the conjecture for several classes of metric spaces including all the Banach spaces with a projectional skeleton, Banach spaces with a w ⁎ -separable dual unit ball and locally separable complete metric spaces.
Authors
- Benjamín Vejnar (ORCID: https://orcid.org/0000-0002-2833-5385)
- Leandro Candido (ORCID: https://orcid.org/0000-0002-6429-3899)
- Marek Cúth (ORCID: https://orcid.org/0000-0001-6688-8004)
Institutions
- Federal Institute of São Paulo (BR)
- Charles University (CZ)
- Departamento de Ciência e Tecnologia (BR)
- Universidade Federal de São Paulo (BR)
Publication Details
- Journal
- Journal of Functional Analysis
- Published
- 2025-03-05
- DOI
- https://doi.org/10.1016/j.jfa.2025.110925
- Primary Topic
- Advanced Banach Space Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00