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Hölder seminorm preserving linear bijections and isometries
dc.contributor.author | Jiménez Vargas, Antonio | |
dc.contributor.author | Navarro Pascual, Miguel Angel | |
dc.date.accessioned | 2024-05-23T10:46:17Z | |
dc.date.available | 2024-05-23T10:46:17Z | |
dc.date.issued | 2008-07-26 | |
dc.identifier.citation | Proc. Indian Acad. Sci. Math. Sci. 119 (2009), no. 1, 53–62 | es_ES |
dc.identifier.issn | 0253-4142 | |
dc.identifier.uri | http://hdl.handle.net/10835/16565 | |
dc.description.abstract | Let (X,d) be a compact metric and 0<α<1. The space Lip^α(X) of Hölder functions of order α is the Banach space of all functions f from X into K such that ||f||=max{||f||_∞, L(f )}<∞, where L(f)=sup{|f(x)−f(y)|/d^α(x, y): x,y ∈ X, x\neq y} is the Hölder seminorm of f. The closed subspace of functions f such that lim_{d(x,y)→0}|f(x)-f (y)|/d^α(x,y)=0 is denoted by lip^α(X). We determine the form of all bijective linear maps from lip^α(X) onto lip^α(Y ) that preserve the Hölder seminorm. | es_ES |
dc.language.iso | en | es_ES |
dc.publisher | Springer | es_ES |
dc.rights | Attribution-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nd/4.0/ | * |
dc.subject | Lipschitz function | es_ES |
dc.subject | Isometry | es_ES |
dc.subject | Linear preserver problem | es_ES |
dc.subject | Banach-Stone theorem | es_ES |
dc.title | Hölder seminorm preserving linear bijections and isometries | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.relation.publisherversion | https://doi.org/10.1007/s12044-009-0006-3 | es_ES |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es_ES |