Compact reduction in Lipschitz-free spaces

Affiliation auteursAffiliation ok
TitreCompact reduction in Lipschitz-free spaces
Type de publicationJournal Article
Year of Publication2021
AuteursAliaga RJ, Nous C, Petitjean C, Prochazka A
JournalPROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
Volume151
PaginationPII S0308210520000670
Date PublishedDEC
Type of ArticleArticle
ISSN0308-2105
Mots-clésApproximation property, Dunford-Pettis property, Lipschitz function, Lipschitz lifting property, Lipschitz-free space, Schur property, weak sequential completeness
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: F(X) is weakly sequentially complete for every superreflexive Banach space X, and F(M) has the Schur property and the approximation property for every scattered complete metric space M.

DOI10.1017/prm.2020.67