000130193 001__ 130193 000130193 005__ 20241125101141.0 000130193 0247_ $$2doi$$a10.1007/s40840-023-01467-5 000130193 0248_ $$2sideral$$a132883 000130193 037__ $$aART-2023-132883 000130193 041__ $$aeng 000130193 100__ $$0(orcid)0000-0001-9211-4475$$aGarcía-Lirola, Luis C.$$uUniversidad de Zaragoza 000130193 245__ $$aInjectivity of Lipschitz Operators 000130193 260__ $$c2023 000130193 5060_ $$aAccess copy available to the general public$$fUnrestricted 000130193 5203_ $$aAny 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. 000130193 536__ $$9info:eu-repo/grantAgreement/ES/AEI-FEDER/ MTM2017-83262-C2-2-P$$9info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2021-122126NB-C32 000130193 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000130193 590__ $$a1.0$$b2023 000130193 592__ $$a0.508$$b2023 000130193 591__ $$aMATHEMATICS$$b117 / 490 = 0.239$$c2023$$dQ1$$eT1 000130193 593__ $$aMathematics (miscellaneous)$$c2023$$dQ2 000130193 594__ $$a2.4$$b2023 000130193 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000130193 700__ $$aPetitjean, Colin 000130193 700__ $$aProcházka, Antonín 000130193 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático 000130193 773__ $$g46, 2 (2023), [31 pp.]$$pBulletin of the Malaysian Mathematical Sciences Society$$tBulletin of the Malaysian Mathematical Sciences Society$$x0126-6705 000130193 8564_ $$s457346$$uhttps://zaguan.unizar.es/record/130193/files/texto_completo.pdf$$yPostprint$$zinfo:eu-repo/semantics/openAccess 000130193 8564_ $$s1502358$$uhttps://zaguan.unizar.es/record/130193/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint$$zinfo:eu-repo/semantics/openAccess 000130193 909CO $$ooai:zaguan.unizar.es:130193$$particulos$$pdriver 000130193 951__ $$a2024-11-22-12:02:48 000130193 980__ $$aARTICLE