2015/07/09 by Peter Hájek, Gilles Lancien, Hájek, Petr +3 · 4 citations
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.1507.02701
openalex publication_date 2015/07/09 · openalex created_date 2022/08/27 · openalex updated_date 2026/07/28
We prove that for any separable Banach space X, there exists a\ncompact metric space which is homeomorphic to the Cantor space and\nwhose Lipschitz-free space contains a complemented subspace isomorphic\nto X. As a consequence we give an example of a compact metric space\nwhich is homeomorphic to the Cantor space and whose Lipschitz-free\nspace fails the approximation property and we prove that there exists\nan uncountable family of topologically equivalent distances on the\nCantor space whose free spaces are pairwise non isomorphic. We also\nprove that the free space over a countable compact metric space has\nthe Schur property. These results answer questions by G. Godefroy.