Metric and homogeneous structure of closed range operators

Autores
Corach, Gustavo; Maestripieri, Alejandra Laura; Mbekhta, Mostafa
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let CR be the set of all bounded linear operators between Hilbert spaces H, K with closed range. This paper is devoted to the study of the topological properties of CR if certain natural metrics are considered on it. We also define an action of the group GH × GK on CR and determine the orbits of this action. These orbits, which are strongly related to the connected components for the topology defined by the metrics mentioned above, determine a stratification of the set of Fredholm and semi-Fredholm operators. Finally, we calculate the distance, with respect to some of the metrics mentioned above, between different orbits of CR.
Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Mbekhta, Mostafa. Universite Lille; Francia
Materia
CLOSED RANGE
PARTIAL ISOMETRY
SEMI-FREDHOLM OPERATORS
POSITIVE OPERATORS
ORBITS
MOORE–PENROSE INVERSE
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:11336/150677
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/150677
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Metric and homogeneous structure of closed range operatorsCorach, GustavoMaestripieri, Alejandra LauraMbekhta, MostafaCLOSED RANGEPARTIAL ISOMETRYSEMI-FREDHOLM OPERATORSPOSITIVE OPERATORSORBITSMOORE–PENROSE INVERSEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let CR be the set of all bounded linear operators between Hilbert spaces H, K with closed range. This paper is devoted to the study of the topological properties of CR if certain natural metrics are considered on it. We also define an action of the group GH × GK on CR and determine the orbits of this action. These orbits, which are strongly related to the connected components for the topology defined by the metrics mentioned above, determine a stratification of the set of Fredholm and semi-Fredholm operators. Finally, we calculate the distance, with respect to some of the metrics mentioned above, between different orbits of CR.Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Mbekhta, Mostafa. Universite Lille; FranciaTheta Foundation2009-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/150677Corach, Gustavo; Maestripieri, Alejandra Laura; Mbekhta, Mostafa; Metric and homogeneous structure of closed range operators; Theta Foundation; Journal of Operator Theory; 61; 1; 8-2009; 171-1900379-40241841-7744CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.theta.ro/jot.htmlinfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/math/0509328info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:26:44Zoai:ri.conicet.gov.ar:11336/150677instacron: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 10:26:44.355CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Metric and homogeneous structure of closed range operators
title Metric and homogeneous structure of closed range operators
spellingShingle Metric and homogeneous structure of closed range operators
Corach, Gustavo
CLOSED RANGE
PARTIAL ISOMETRY
SEMI-FREDHOLM OPERATORS
POSITIVE OPERATORS
ORBITS
MOORE–PENROSE INVERSE
title_short Metric and homogeneous structure of closed range operators
title_full Metric and homogeneous structure of closed range operators
title_fullStr Metric and homogeneous structure of closed range operators
title_full_unstemmed Metric and homogeneous structure of closed range operators
title_sort Metric and homogeneous structure of closed range operators
dc.creator.none.fl_str_mv Corach, Gustavo
Maestripieri, Alejandra Laura
Mbekhta, Mostafa
author Corach, Gustavo
author_facet Corach, Gustavo
Maestripieri, Alejandra Laura
Mbekhta, Mostafa
author_role author
author2 Maestripieri, Alejandra Laura
Mbekhta, Mostafa
author2_role author
author
dc.subject.none.fl_str_mv CLOSED RANGE
PARTIAL ISOMETRY
SEMI-FREDHOLM OPERATORS
POSITIVE OPERATORS
ORBITS
MOORE–PENROSE INVERSE
topic CLOSED RANGE
PARTIAL ISOMETRY
SEMI-FREDHOLM OPERATORS
POSITIVE OPERATORS
ORBITS
MOORE–PENROSE INVERSE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let CR be the set of all bounded linear operators between Hilbert spaces H, K with closed range. This paper is devoted to the study of the topological properties of CR if certain natural metrics are considered on it. We also define an action of the group GH × GK on CR and determine the orbits of this action. These orbits, which are strongly related to the connected components for the topology defined by the metrics mentioned above, determine a stratification of the set of Fredholm and semi-Fredholm operators. Finally, we calculate the distance, with respect to some of the metrics mentioned above, between different orbits of CR.
Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Mbekhta, Mostafa. Universite Lille; Francia
description Let CR be the set of all bounded linear operators between Hilbert spaces H, K with closed range. This paper is devoted to the study of the topological properties of CR if certain natural metrics are considered on it. We also define an action of the group GH × GK on CR and determine the orbits of this action. These orbits, which are strongly related to the connected components for the topology defined by the metrics mentioned above, determine a stratification of the set of Fredholm and semi-Fredholm operators. Finally, we calculate the distance, with respect to some of the metrics mentioned above, between different orbits of CR.
publishDate 2009
dc.date.none.fl_str_mv 2009-08
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/11336/150677
Corach, Gustavo; Maestripieri, Alejandra Laura; Mbekhta, Mostafa; Metric and homogeneous structure of closed range operators; Theta Foundation; Journal of Operator Theory; 61; 1; 8-2009; 171-190
0379-4024
1841-7744
CONICET Digital
CONICET
url http://hdl.handle.net/11336/150677
identifier_str_mv Corach, Gustavo; Maestripieri, Alejandra Laura; Mbekhta, Mostafa; Metric and homogeneous structure of closed range operators; Theta Foundation; Journal of Operator Theory; 61; 1; 8-2009; 171-190
0379-4024
1841-7744
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://www.theta.ro/jot.html
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/math/0509328
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
application/pdf
dc.publisher.none.fl_str_mv Theta Foundation
publisher.none.fl_str_mv Theta Foundation
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
_version_ 1844614268557721600
score 13.070432

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