English

Compact reduction in Lipschitz free spaces

Functional Analysis 2021-08-12 v3

Abstract

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: F(X)\mathcal F(X) is weakly sequentially complete for every superreflexive Banach space XX, and F(M)\mathcal F(M) has the Schur property and the approximation property for every scattered complete metric space MM.

Keywords

Cite

@article{arxiv.2004.14250,
  title  = {Compact reduction in Lipschitz free spaces},
  author = {Ramón J. Aliaga and Camille Noûs and Colin Petitjean and Antonín Procházka},
  journal= {arXiv preprint arXiv:2004.14250},
  year   = {2021}
}
R2 v1 2026-06-23T15:11:12.030Z