Lattice Lipschitz operators on C(K)- spaces

[EN] Given a Banach lattice L, the space of lattice Lipschitz operators on L has been introduced as a natural Lipschitz generalization of the linear notions of diagonal operator and multiplication operator on Banach function lattices. It is a particular space of superposition operators on Banach lat...

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Autores: Arnau, Roger|||0000-0003-2544-8875, Calabuig, J. M.|||0000-0001-8398-8664, Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/232255
Acceso en línea:https://riunet.upv.es/handle/10251/232255
Access Level:acceso abierto
Palabra clave:Lipschitz function
Continuous function
C(K)
Lattice Lipschitz
Non-linear operator
Banach lattice
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spelling Lattice Lipschitz operators on C(K)- spacesArnau, Roger|||0000-0003-2544-8875Calabuig, J. M.|||0000-0001-8398-8664Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154Lipschitz functionContinuous functionC(K)Lattice LipschitzNon-linear operatorBanach lattice[EN] Given a Banach lattice L, the space of lattice Lipschitz operators on L has been introduced as a natural Lipschitz generalization of the linear notions of diagonal operator and multiplication operator on Banach function lattices. It is a particular space of superposition operators on Banach lattices. Motivated by certain procedures in Reinforcement Learning based on McShane-Whitney extensions of Lipschitz maps, this class has proven to be useful also in the classical context of Mathematical Analysis. In this paper, we discuss the properties of such operators when defined on spaces of continuous functions, focusing attention on the functional bounds for the pointwise Lipschitz inequalities defining the lattice Lipschitz operators, the representation theorems for these operators as vector-valued functions, and the corresponding dual spaces. Finally, and with possible applications in Artificial Intelligence in mind, we provide a McShane-Whitney extension theorem for these operators.This article is funded by Universitat Politècnica de València (PAID-01-21), Ministerio de Ciencia e Innovación (PID2022-138342NB-I00). Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.Duke University PressDepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería de Caminos, Canales y PuertosEscuela Técnica Superior de Ingeniería IndustrialAgencia Estatal de InvestigaciónUniversitat Politècnica de ValènciaRepositorio Institucional de la Universitat Politècnica de València Riunet20252025-04-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/232255reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023 PID2022-138342NB-I00 TECNICAS DE ANALISIS FUNCIONAL EN PROBLEMAS DE APROXIMACION Y APLICACIONESUniversitat Politècnica de València https://doi.org/10.13039/501100004233 PAID-01-21open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2322552026-06-13T07:49:27Z
dc.title.none.fl_str_mv Lattice Lipschitz operators on C(K)- spaces
title Lattice Lipschitz operators on C(K)- spaces
spellingShingle Lattice Lipschitz operators on C(K)- spaces
Arnau, Roger|||0000-0003-2544-8875
Lipschitz function
Continuous function
C(K)
Lattice Lipschitz
Non-linear operator
Banach lattice
title_short Lattice Lipschitz operators on C(K)- spaces
title_full Lattice Lipschitz operators on C(K)- spaces
title_fullStr Lattice Lipschitz operators on C(K)- spaces
title_full_unstemmed Lattice Lipschitz operators on C(K)- spaces
title_sort Lattice Lipschitz operators on C(K)- spaces
dc.creator.none.fl_str_mv Arnau, Roger|||0000-0003-2544-8875
Calabuig, J. M.|||0000-0001-8398-8664
Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154
author Arnau, Roger|||0000-0003-2544-8875
author_facet Arnau, Roger|||0000-0003-2544-8875
Calabuig, J. M.|||0000-0001-8398-8664
Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154
author_role author
author2 Calabuig, J. M.|||0000-0001-8398-8664
Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería de Caminos, Canales y Puertos
Escuela Técnica Superior de Ingeniería Industrial
Agencia Estatal de Investigación
Universitat Politècnica de València
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Lipschitz function
Continuous function
C(K)
Lattice Lipschitz
Non-linear operator
Banach lattice
topic Lipschitz function
Continuous function
C(K)
Lattice Lipschitz
Non-linear operator
Banach lattice
description [EN] Given a Banach lattice L, the space of lattice Lipschitz operators on L has been introduced as a natural Lipschitz generalization of the linear notions of diagonal operator and multiplication operator on Banach function lattices. It is a particular space of superposition operators on Banach lattices. Motivated by certain procedures in Reinforcement Learning based on McShane-Whitney extensions of Lipschitz maps, this class has proven to be useful also in the classical context of Mathematical Analysis. In this paper, we discuss the properties of such operators when defined on spaces of continuous functions, focusing attention on the functional bounds for the pointwise Lipschitz inequalities defining the lattice Lipschitz operators, the representation theorems for these operators as vector-valued functions, and the corresponding dual spaces. Finally, and with possible applications in Artificial Intelligence in mind, we provide a McShane-Whitney extension theorem for these operators.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-04-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/232255
url https://riunet.upv.es/handle/10251/232255
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023 PID2022-138342NB-I00 TECNICAS DE ANALISIS FUNCIONAL EN PROBLEMAS DE APROXIMACION Y APLICACIONES
Universitat Politècnica de València https://doi.org/10.13039/501100004233 PAID-01-21
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Duke University Press
publisher.none.fl_str_mv Duke University Press
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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