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Article Dans Une Revue Studia Mathematica Année : 2021

Compact reduction in Lipschitz free spaces

Résumé

We prove a general principle satisfied by weakly precompact sets of Lipschitz-free spaces. By this principle, certain infinite dimensional phenomena in Lipschitz-free spaces over general metric spaces may be reduced to the same phenomena in free spaces over their compact subsets. As easy consequences we derive several new and some known results. The main new results are: $\mathcal F(X)$ is weakly sequentially complete for every superreflexive Banach space $X$, and $\mathcal F(M)$ has the Schur property for every scattered complete metric space $M$.
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Dates et versions

hal-02558998 , version 1 (22-10-2020)

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Ramón J. Aliaga, Camille Noûs, Colin Petitjean, Antonin Prochazka. Compact reduction in Lipschitz free spaces. Studia Mathematica, 2021, ⟨10.4064/sm200925-18-1⟩. ⟨hal-02558998⟩
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