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Into linear isometries between spaces of Lipschitz functions
dc.contributor.author | Jiménez Vargas, Antonio | |
dc.contributor.author | Villegas Vallecillos, Moisés | |
dc.date.accessioned | 2024-05-23T11:12:04Z | |
dc.date.available | 2024-05-23T11:12:04Z | |
dc.date.issued | 2007-03-03 | |
dc.identifier.citation | Houston J. Math. 34 (2008), no. 4, 1165–1184 | es_ES |
dc.identifier.issn | 0362-1588 | |
dc.identifier.uri | http://hdl.handle.net/10835/16572 | |
dc.description.abstract | In this paper we state a Lipschitz version of a known Holsztynski's theorem on linear isometries of C(X)-spaces. Let Lip(X) be the Banach space of all scalar-valued Lipschitz functions f on a compact metric space X endowed with the norm ||f||=max{||f||_\infty, L(f)}, where L(f) is the Lipschitz constant of f. We prove that any linear isometry T from Lip(X) into Lip(Y) satisfying that L(T(1_X))<1 is essentially a weighted composition operator in the form Tf(y)=\tau(y)f(\varphi(y)) for all f in Lip(X) and y in Y_0, where Y_0 is a closed subset of Y, \varphi is a Lipschitz map from Y_0 onto X with L(\varphi) less or equal than max{1,diam(X)}, and \tau is a function in Lip(Y) with ||\tau||=1 and |\tau(y)|= 1 for all y in Y_0. We improve this representation in the case of onto linear isometries and we classify codimension 1 linear isometries in two types. | es_ES |
dc.language.iso | en | es_ES |
dc.publisher | University of Houston, Houston, Texas | es_ES |
dc.rights | Attribution-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nd/4.0/ | * |
dc.subject | Linear isometry | es_ES |
dc.subject | Lipschitz function | es_ES |
dc.subject | Finite codimension | es_ES |
dc.title | Into linear isometries between spaces of Lipschitz functions | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.relation.publisherversion | https://doi.org/10.1016/j.eswa.2007.05.039 | es_ES |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es_ES |