Proper splittings of Hilbert space operators

Autores
Fongi, Guillermina; Gonzalez, Maria Celeste
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear operators defined on Hilbert spaces. We study the convergence of general proper splittings of operators in the infinite dimensional context. We also propose some particular splittings for special classes of operators and we study different criteria of convergence and comparison for them. In some cases, these criteria are given under hypothesis of operator order relations. In addition, we relate these results with the concept of the symmetric approximation of a frame in a Hilbert space.
Fil: Fongi, Guillermina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
Fil: Gonzalez, Maria Celeste. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento; Argentina
Materia
HILBERT SPACE OPERATORS
SPLITTINGS
ITERATIVE METHODS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/263366
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/263366
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Proper splittings of Hilbert space operatorsFongi, GuillerminaGonzalez, Maria CelesteHILBERT SPACE OPERATORSSPLITTINGSITERATIVE METHODShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear operators defined on Hilbert spaces. We study the convergence of general proper splittings of operators in the infinite dimensional context. We also propose some particular splittings for special classes of operators and we study different criteria of convergence and comparison for them. In some cases, these criteria are given under hypothesis of operator order relations. In addition, we relate these results with the concept of the symmetric approximation of a frame in a Hilbert space.Fil: Fongi, Guillermina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: Gonzalez, Maria Celeste. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento; ArgentinaAcademic Press Inc Elsevier Science2025-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/263366Fongi, Guillermina; Gonzalez, Maria Celeste; Proper splittings of Hilbert space operators; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 545; 1; 5-2025; 1-190022-247XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://linkinghub.elsevier.com/retrieve/pii/S0022247X24010151info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2024.129093info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2403.10247info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:23:52Zoai:ri.conicet.gov.ar:11336/263366instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:23:52.994CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Proper splittings of Hilbert space operators
title Proper splittings of Hilbert space operators
spellingShingle Proper splittings of Hilbert space operators
Fongi, Guillermina
HILBERT SPACE OPERATORS
SPLITTINGS
ITERATIVE METHODS
title_short Proper splittings of Hilbert space operators
title_full Proper splittings of Hilbert space operators
title_fullStr Proper splittings of Hilbert space operators
title_full_unstemmed Proper splittings of Hilbert space operators
title_sort Proper splittings of Hilbert space operators
dc.creator.none.fl_str_mv Fongi, Guillermina
Gonzalez, Maria Celeste
author Fongi, Guillermina
author_facet Fongi, Guillermina
Gonzalez, Maria Celeste
author_role author
author2 Gonzalez, Maria Celeste
author2_role author
dc.subject.none.fl_str_mv HILBERT SPACE OPERATORS
SPLITTINGS
ITERATIVE METHODS
topic HILBERT SPACE OPERATORS
SPLITTINGS
ITERATIVE METHODS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear operators defined on Hilbert spaces. We study the convergence of general proper splittings of operators in the infinite dimensional context. We also propose some particular splittings for special classes of operators and we study different criteria of convergence and comparison for them. In some cases, these criteria are given under hypothesis of operator order relations. In addition, we relate these results with the concept of the symmetric approximation of a frame in a Hilbert space.
Fil: Fongi, Guillermina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
Fil: Gonzalez, Maria Celeste. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento; Argentina
description Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear operators defined on Hilbert spaces. We study the convergence of general proper splittings of operators in the infinite dimensional context. We also propose some particular splittings for special classes of operators and we study different criteria of convergence and comparison for them. In some cases, these criteria are given under hypothesis of operator order relations. In addition, we relate these results with the concept of the symmetric approximation of a frame in a Hilbert space.
publishDate 2025
dc.date.none.fl_str_mv 2025-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/263366
Fongi, Guillermina; Gonzalez, Maria Celeste; Proper splittings of Hilbert space operators; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 545; 1; 5-2025; 1-19
0022-247X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/263366
identifier_str_mv Fongi, Guillermina; Gonzalez, Maria Celeste; Proper splittings of Hilbert space operators; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 545; 1; 5-2025; 1-19
0022-247X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://linkinghub.elsevier.com/retrieve/pii/S0022247X24010151
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2024.129093
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2403.10247
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.069144

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