Embeddings of Lipschitz-free spaces into ℓ1
| Autor: | Antonín Procházka, Ramón J. Aliaga, Colin Petitjean |
|---|---|
| Přispěvatelé: | PETITJEAN, Colin, Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Université de Bourgogne (UB)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse et Mathématiques Appliquées (LAMA), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS)-Université de Bourgogne (UB) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Unit sphere
Lipschitz homeomorphism Closure (topology) Lipschitz-free space 46B20 05C05 46B25 54C25 [MATH] Mathematics [math] Extreme point [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 01 natural sciences Measure (mathematics) Complete metric space Separable space TECNOLOGIA ELECTRONICA Combinatorics 0103 physical sciences FOS: Mathematics [MATH.MATH-MG] Mathematics [math]/Metric Geometry [math.MG] [MATH]Mathematics [math] 0101 mathematics [MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG] ComputingMilieux_MISCELLANEOUS Mathematics 010102 general mathematics [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA] Lipschitz continuity Linear subspace Functional Analysis (math.FA) Mathematics - Functional Analysis R-tree 010307 mathematical physics Analysis |
| Zdroj: | Journal of Functional Analysis Journal of Functional Analysis, Elsevier, 2021, 280 (6), pp.108916. ⟨10.1016/j.jfa.2020.108916⟩ Journal of Functional Analysis, Elsevier, 2021, 280 (6), pp.108916 RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname |
| ISSN: | 0022-1236 1096-0783 |
| DOI: | 10.1016/j.jfa.2020.108916⟩ |
| Popis: | [EN] We show that, for a separable and complete metric space $M$, the Lipschitz-free space $\mathcal{F}(M)$ embeds linearly and almost-isometrically into $\ell_1$ if and only if $M$ is a subset of an $\mathbb{R}$-tree with length measure 0. Moreover, it embeds isometrically if and only if the length measure of the closure of the set of branching points of $M$ (taken in any minimal $\mathbb{R}$-tree that contains $M$) is also 0. We also prove that, for subspaces of $L_1$ spaces, every extreme point of the unit ball is preserved; as a consequence we obtain a complete characterization of extreme points of the unit ball of $\mathcal{F}(M)$ when $M$ is a subset of an $\mathbb{R}$-tree. This work was supported by the French "Investissements d'Avenir" program, project ISITE-BFC (contract ANR-15-IDEX-03, funding agency: Secretariat general pour l'investissement). R. J. Aliaga was also partially supported by the Spanish Ministry of Economy, Industry and Competitiveness under Grant MTM2017-83262-C2-2-P. The authors would like to thank Abraham Rueda Zoca for his valuable suggestions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect