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A note on nonseparable Lipschitz-free spaces

Ramón J. Aliaga, Guillaume Grelier, Antonín Procházka (2024)

Commentationes Mathematicae Universitatis Carolinae

We prove that several classical Banach space properties are equivalent to separability for the class of Lipschitz-free spaces, including Corson’s property ( 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 nonseparable Lipschitz-free spaces have a weak * sequentially compact ball is undecidable in ZFC. Finally, we provide an...

A note on the Poincaré inequality

Alireza Ranjbar-Motlagh (2003)

Studia Mathematica

The Poincaré inequality is extended to uniformly doubling metric-measure spaces which satisfy a version of the triangle comparison property. The proof is based on a generalization of the change of variables formula.

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