Approximation properties and Schauder decompositions in Lipschitz-free spaces.

Gilles Lancien (1) , Eva Pernecka (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 Department of Mathematical Analysis, Charles University.

We prove that the Lipschitz-free space over a doubling metric space has the bounded approximation property. We also show that the Lipschitz-free space over the space of summable sequences has a monotone fi nite-dimensional Schauder decomposition.

Domaines: Analyse fonctionnelle [math.FA]

Gilles Lancien, Eva Pernecka. Approximation properties and Schauder decompositions in Lipschitz-free spaces.. Journal of Functional Analysis, 2013, 264, pp.2323-2334. ⟨hal-00825060⟩