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arXiv · 2406.03982

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

Leandro Candido·Marek Cuth·Benjamin Vejnar
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Abstract

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.

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Leandro Candido, Marek Cuth, Benjamin Vejnar. 2024-06-06. On the weak$^*$ separability of the space of Lipschitz functions. https://doi.org/10.1016/j.jfa.2025.110925

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