Year: 2025
Type: article
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 Gâteaux 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-Nikodým property.
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G121809054, G1422035950, G1622782223, Free space Isomorphisms and Isometries, G1855990336, G2146289210, G2262748287, G2573088050, G2660406951, G3038777702, G3145880764, G3480869486, G3681454997, G4042783231, G4087428547, G425668148, G451917667, G5126555218, G5421974903, G5967599077, G6982000174, G7084143925, G7594723714, G8383811633, G843564687
OpenAlex ID: W4410414782