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A note on copies of c 0 in spaces of weak* measurable functions

Juan Carlos Ferrando (2000)

Commentationes Mathematicae Universitatis Carolinae

If ( Ω , Σ , μ ) is a finite measure space and X a Banach space, in this note we show that L w * 1 ( μ , X * ) , the Banach space of all classes of weak* equivalent X * -valued weak* measurable functions f defined on Ω such that f ( ω ) g ( ω ) a.e. for some g L 1 ( μ ) equipped with its usual norm, contains a copy of c 0 if and only if X * contains a copy of c 0 .

A Note on Div-Curl Lemma

Gala, Sadek (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 42B30, 46E35, 35B65.We prove two results concerning the div-curl lemma without assuming any sort of exact cancellation, namely the divergence and curl need not be zero, and d i v ( u v ) H 1 ( R d ) which include as a particular case, the result of [3].

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...

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