Operator Least Squares Problems and Moore–Penrose Inverses in Krein Spaces

Given a Krein space H and B, C in L(H), L(H), the bounded linear operators on H, the minimization/maximization of expressions of the form (BX−C)#(BX−C) as X runs over L(H) is studied. Complete solutions are found for the problems posed, including solvability criteria and a characterization of the so...

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Detalles Bibliográficos
Autores: Contino, Maximiliano, Maestripieri, Alejandra Laura, Marcantognini Palacios, Stefania Alma María
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/88408
Acceso en línea:http://hdl.handle.net/11336/88408
Access Level:acceso abierto
Palabra clave:OPERATOR APPROXIMATION
KREIN SPACES
MOORE-PENROSE INVERSES
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Operator Least Squares Problems and Moore–Penrose Inverses in Krein SpacesContino, MaximilianoMaestripieri, Alejandra LauraMarcantognini Palacios, Stefania Alma MaríaOPERATOR APPROXIMATIONKREIN SPACESMOORE-PENROSE INVERSEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given a Krein space H and B, C in L(H), L(H), the bounded linear operators on H, the minimization/maximization of expressions of the form (BX−C)#(BX−C) as X runs over L(H) is studied. Complete solutions are found for the problems posed, including solvability criteria and a characterization of the solutions when they exist. Min-max problems associated to Krein space decompositions of B are also considered, leading to a characterization of the Moore-Penrose inverse as the unique solution of a variational problem. Other generalized inverses are similarly described.Fil: Contino, Maximiliano. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Matemáticas; ArgentinaFil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Matemáticas; ArgentinaFil: Marcantognini Palacios, Stefania Alma María. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Instituto Venezolano de Investigaciones Científicas; VenezuelaBirkhauser Verlag Ag2018-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/88408Contino, Maximiliano; Maestripieri, Alejandra Laura; Marcantognini Palacios, Stefania Alma María; Operator Least Squares Problems and Moore–Penrose Inverses in Krein Spaces; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 90; 3; 6-2018; 1-230378-620X1420-8989CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s00020-018-2456-4info:eu-repo/semantics/altIdentifier/doi/10.1007%2Fs00020-018-2456-4info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1711.08787info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T14:15:23Zoai:ri.conicet.gov.ar:11336/88408instacron: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:34982024-05-08 14:15:23.937CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Operator Least Squares Problems and Moore–Penrose Inverses in Krein Spaces
title Operator Least Squares Problems and Moore–Penrose Inverses in Krein Spaces
spellingShingle Operator Least Squares Problems and Moore–Penrose Inverses in Krein Spaces
Contino, Maximiliano
OPERATOR APPROXIMATION
KREIN SPACES
MOORE-PENROSE INVERSES
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Operator Least Squares Problems and Moore–Penrose Inverses in Krein Spaces
title_full Operator Least Squares Problems and Moore–Penrose Inverses in Krein Spaces
title_fullStr Operator Least Squares Problems and Moore–Penrose Inverses in Krein Spaces
title_full_unstemmed Operator Least Squares Problems and Moore–Penrose Inverses in Krein Spaces
title_sort Operator Least Squares Problems and Moore–Penrose Inverses in Krein Spaces
dc.creator.none.fl_str_mv Contino, Maximiliano
Maestripieri, Alejandra Laura
Marcantognini Palacios, Stefania Alma María
author Contino, Maximiliano
author_facet Contino, Maximiliano
Maestripieri, Alejandra Laura
Marcantognini Palacios, Stefania Alma María
author_role author
author2 Maestripieri, Alejandra Laura
Marcantognini Palacios, Stefania Alma María
author2_role author
author
dc.subject.none.fl_str_mv OPERATOR APPROXIMATION
KREIN SPACES
MOORE-PENROSE INVERSES
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic OPERATOR APPROXIMATION
KREIN SPACES
MOORE-PENROSE INVERSES
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description Given a Krein space H and B, C in L(H), L(H), the bounded linear operators on H, the minimization/maximization of expressions of the form (BX−C)#(BX−C) as X runs over L(H) is studied. Complete solutions are found for the problems posed, including solvability criteria and a characterization of the solutions when they exist. Min-max problems associated to Krein space decompositions of B are also considered, leading to a characterization of the Moore-Penrose inverse as the unique solution of a variational problem. Other generalized inverses are similarly described.
publishDate 2018
dc.date.none.fl_str_mv 2018-06
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/11336/88408
Contino, Maximiliano; Maestripieri, Alejandra Laura; Marcantognini Palacios, Stefania Alma María; Operator Least Squares Problems and Moore–Penrose Inverses in Krein Spaces; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 90; 3; 6-2018; 1-23
0378-620X
1420-8989
CONICET Digital
CONICET
url http://hdl.handle.net/11336/88408
identifier_str_mv Contino, Maximiliano; Maestripieri, Alejandra Laura; Marcantognini Palacios, Stefania Alma María; Operator Least Squares Problems and Moore–Penrose Inverses in Krein Spaces; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 90; 3; 6-2018; 1-23
0378-620X
1420-8989
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s00020-018-2456-4
info:eu-repo/semantics/altIdentifier/doi/10.1007%2Fs00020-018-2456-4
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1711.08787
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Birkhauser Verlag Ag
publisher.none.fl_str_mv Birkhauser Verlag Ag
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15,811543

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