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Linear bijections preserving the Hölder seminorm
dc.contributor.author | Jiménez Vargas, Antonio | |
dc.date.accessioned | 2024-05-23T11:22:41Z | |
dc.date.available | 2024-05-23T11:22:41Z | |
dc.date.issued | 2007-03-21 | |
dc.identifier.citation | Proc. Amer. Math. Soc. 135 (2007), no. 8, 2539–2547 | es_ES |
dc.identifier.issn | 0002-9939 | |
dc.identifier.uri | http://hdl.handle.net/10835/16577 | |
dc.description.abstract | Let (X,d) be a compact metric space and let α be a real number with 0 < α < 1. The aim of this paper is to solve a linear preserver problem on the Banach algebra C^α(X) of Hölder functions of order α from X into K. We show that each linear bijection T : C^α(X) → C^α(X) having the property that α(T(f))=α(f) for every f ∈ C^α(X), where α(f)=sup{|f(x)-f(y)|/d(x, y)^α: x, y ∈ X, x \neq y}, is of the form T(f) = τf ◦ϕ+μ(f)1_X for every f ∈ C^α(X), where τ ∈ K with |τ| = 1, ϕ : X → X is a surjective isometry and μ : C^α(X) → K is a linear functional. | es_ES |
dc.language.iso | en | es_ES |
dc.publisher | American Mathematical Society | es_ES |
dc.rights | Attribution-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nd/4.0/ | * |
dc.subject | Linear preserver problem | es_ES |
dc.subject | Extreme point, isometry | es_ES |
dc.title | Linear bijections preserving the Hölder seminorm | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.relation.publisherversion | https://doi.org/10.1090/S0002-9939-07-08756-4 | es_ES |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es_ES |