130193 20241125101141.0 doi 10.1007/s40840-023-01467-5 sideral 132883 ART-2023-132883 eng García-Lirola, Luis C. Universidad de Zaragoza (orcid)0000-0001-9211-4475 Injectivity of Lipschitz Operators 2023 Access copy available to the general public Unrestricted Any Lipschitz map f:M→N between metric spaces can be “linearised” in such a way that it becomes a bounded linear operator fˆ:F(M)→F(N) between the Lipschitz-free spaces over M and N. The purpose of this note is to explore the connections between the injectivity of f and the injectivity of fˆ. While it is obvious that if fˆ is injective then so is f, the converse is less clear. Indeed, we pin down some cases where this implication does not hold but we also prove that, for some classes of metric spaces M, any injective Lipschitz map f:M→N (for any N) admits an injective linearisation. Along our way, we study how Lipschitz maps carry the support of elements in free spaces and also we provide stronger conditions on f which ensure that fˆ is injective. info:eu-repo/grantAgreement/ES/AEI-FEDER/ MTM2017-83262-C2-2-P info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2021-122126NB-C32 info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 1.0 2023 MATHEMATICS 117 / 490 = 0.239 2023 Q1 T1 0.508 2023 Mathematics (miscellaneous) 2023 Q2 2.4 2023 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Petitjean, Colin Procházka, Antonín 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 46, 2 (2023), [31 pp.] Bulletin of the Malaysian Mathematical Sciences Society Bulletin of the Malaysian Mathematical Sciences Society 0126-6705 457346 http://zaguan.unizar.es/record/130193/files/texto_completo.pdf Postprint info:eu-repo/date/embargoEnd/2024-02-01 1502358 http://zaguan.unizar.es/record/130193/files/texto_completo.jpg?subformat=icon icon Postprint info:eu-repo/date/embargoEnd/2024-02-01 oai:zaguan.unizar.es:130193 articulos driver 2024-11-22-12:02:48 ARTICLE