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arXiv · 2312.14678

A note on nonseparable Lipschitz-free spaces

Ramón J. Aliaga·Guillaume Grelier·Antonín Procházka
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Abstract

We prove that several classical Banach space properties are equivalent to separability for the class of Lipschitz-free spaces, including Corson's property ($\mathcal{C}$), Talponen's Countable Separation Property, or being a G\^ateaux differentiability space. On the other hand, we single out more general properties where this equivalence fails. In particular, the question whether the duals of non-separable Lipschitz-free spaces have a weak$^*$ sequentially compact ball is undecidable in ZFC. Finally, we provide an example of a nonseparable dual Lipschitz-free space that fails the Radon-Nikod\'ym property.

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Ramón J. Aliaga, Guillaume Grelier, Antonín Procházka. 2023-12-22. A note on nonseparable Lipschitz-free spaces. https://arxiv.org/abs/2312.14678

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