Isometries on L-2(X) and monotone functions

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/27512

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.contributor	Universitat Politècnica de Catalunya. LARCA - Laboratori d'Algorísmia Relacional, Complexitat i Aprenentatge
dc.contributor.author	Boza Rocho, Santiago
dc.contributor.author	Soria, Javier
dc.date	2014-02-01
dc.identifier.citation	Boza, S.; Soria, J. Isometries on L-2(X) and monotone functions. "Mathematische Nachrichten", 01 Febrer 2014, vol. 287, núm. 2-3, p. 160-172.
dc.identifier.citation	0025-584X
dc.identifier.citation	10.1002/mana.201200346
dc.identifier.uri	http://hdl.handle.net/2117/27512
dc.language.iso	eng
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
dc.subject	Isometrics (Mathematics)
dc.subject	Isometries
dc.subject	Hardy operator
dc.subject	monotone functions
dc.subject	Hardy operator
dc.subject	Minus
dc.subject	Decreasing functions
dc.subject	Measure-spaces
dc.subject	Inequalities
dc.subject	Identity
dc.subject	Cone
dc.subject	Transformacions (Matemàtica)
dc.title	Isometries on L-2(X) and monotone functions
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	We study necessary and sufficient conditions on a bounded operator T defined on the Hilbert space L-2(X) to be an isometry and show that, under suitable hypotheses, it suffices to restrict T to a smaller class of functions (e.g., if X = R+, to the cone of positive and decreasing functions). We also consider the problem of characterizing the sets Y subset of X for which the orthogonal projection of the operator T on L-2(Y) is also an isometry. Finally, we illustrate our results with several examples involving classical operators on different settings. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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