Proper subspaces and compatibility

Autores
Andruchow, Esteban; Chiumiento, Eduardo Hernan; Di Iorio y Lucero, María Eugenia
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let E be a Banach space contained in a Hilbert space L. Assume thatthe inclusion is continuous with dense range. Following the terminology of Gohberg andZambicki, we say that a bounded operator on E is a proper operator if it admits anadjoint with respect to the inner product of L. A proper operator which is self-adjointwith respect to the inner product of L is called symmetrizable. By a proper subspace Swe mean a closed subspace of E which is the range of a proper projection. Furthermore,if there exists a symmetrizable projection onto S, then S belongs to a well-known class ofsubspaces called compatible subspaces. We nd equivalent conditions to describe propersubspaces. Then we prove a necessary and sucient condition for a proper subspace tobe compatible. The existence of non-compatible proper subspaces is related to spectralproperties of symmetrizable operators. Each proper subspace S has a supplement T whichis also a proper subspace.We give a characterization of the compatibility of both subspacesS and T . Several examples are provided that illustrate dierent situations between properand compatible subspaces
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Fil: Di Iorio y Lucero, María Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Materia
PROJECTION
COMPATIBLE SUBSPACE
PROPER OPERATOR
SPECTRUM
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:11336/18930
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Proper subspaces and compatibilityAndruchow, EstebanChiumiento, Eduardo HernanDi Iorio y Lucero, María EugeniaPROJECTIONCOMPATIBLE SUBSPACEPROPER OPERATORSPECTRUMhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let E be a Banach space contained in a Hilbert space L. Assume thatthe inclusion is continuous with dense range. Following the terminology of Gohberg andZambicki, we say that a bounded operator on E is a proper operator if it admits anadjoint with respect to the inner product of L. A proper operator which is self-adjointwith respect to the inner product of L is called symmetrizable. By a proper subspace Swe mean a closed subspace of E which is the range of a proper projection. Furthermore,if there exists a symmetrizable projection onto S, then S belongs to a well-known class ofsubspaces called compatible subspaces. We nd equivalent conditions to describe propersubspaces. Then we prove a necessary and sucient condition for a proper subspace tobe compatible. The existence of non-compatible proper subspaces is related to spectralproperties of symmetrizable operators. Each proper subspace S has a supplement T whichis also a proper subspace.We give a characterization of the compatibility of both subspacesS and T . Several examples are provided that illustrate dierent situations between properand compatible subspacesFil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaFil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaFil: Di Iorio y Lucero, María Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaPolish Acad Sciences Inst Mathematics2015-12info: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/11336/18930Andruchow, Esteban; Chiumiento, Eduardo Hernan; Di Iorio y Lucero, María Eugenia; Proper subspaces and compatibility; Polish Acad Sciences Inst Mathematics; Studia Mathematica; 231; 3; 12-2015; 195-2180039-3223CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/ 10.4064/sm8225-2-2016info:eu-repo/semantics/altIdentifier/url/https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/231/3/91441/proper-subspaces-and-compatibilityinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1503.00596info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:45:35Zoai:ri.conicet.gov.ar:11336/18930instacron: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 10:45:35.816CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Proper subspaces and compatibility
title Proper subspaces and compatibility
spellingShingle Proper subspaces and compatibility
Andruchow, Esteban
PROJECTION
COMPATIBLE SUBSPACE
PROPER OPERATOR
SPECTRUM
title_short Proper subspaces and compatibility
title_full Proper subspaces and compatibility
title_fullStr Proper subspaces and compatibility
title_full_unstemmed Proper subspaces and compatibility
title_sort Proper subspaces and compatibility
dc.creator.none.fl_str_mv Andruchow, Esteban
Chiumiento, Eduardo Hernan
Di Iorio y Lucero, María Eugenia
author Andruchow, Esteban
author_facet Andruchow, Esteban
Chiumiento, Eduardo Hernan
Di Iorio y Lucero, María Eugenia
author_role author
author2 Chiumiento, Eduardo Hernan
Di Iorio y Lucero, María Eugenia
author2_role author
author
dc.subject.none.fl_str_mv PROJECTION
COMPATIBLE SUBSPACE
PROPER OPERATOR
SPECTRUM
topic PROJECTION
COMPATIBLE SUBSPACE
PROPER OPERATOR
SPECTRUM
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 E be a Banach space contained in a Hilbert space L. Assume thatthe inclusion is continuous with dense range. Following the terminology of Gohberg andZambicki, we say that a bounded operator on E is a proper operator if it admits anadjoint with respect to the inner product of L. A proper operator which is self-adjointwith respect to the inner product of L is called symmetrizable. By a proper subspace Swe mean a closed subspace of E which is the range of a proper projection. Furthermore,if there exists a symmetrizable projection onto S, then S belongs to a well-known class ofsubspaces called compatible subspaces. We nd equivalent conditions to describe propersubspaces. Then we prove a necessary and sucient condition for a proper subspace tobe compatible. The existence of non-compatible proper subspaces is related to spectralproperties of symmetrizable operators. Each proper subspace S has a supplement T whichis also a proper subspace.We give a characterization of the compatibility of both subspacesS and T . Several examples are provided that illustrate dierent situations between properand compatible subspaces
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Fil: Di Iorio y Lucero, María Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
description Let E be a Banach space contained in a Hilbert space L. Assume thatthe inclusion is continuous with dense range. Following the terminology of Gohberg andZambicki, we say that a bounded operator on E is a proper operator if it admits anadjoint with respect to the inner product of L. A proper operator which is self-adjointwith respect to the inner product of L is called symmetrizable. By a proper subspace Swe mean a closed subspace of E which is the range of a proper projection. Furthermore,if there exists a symmetrizable projection onto S, then S belongs to a well-known class ofsubspaces called compatible subspaces. We nd equivalent conditions to describe propersubspaces. Then we prove a necessary and sucient condition for a proper subspace tobe compatible. The existence of non-compatible proper subspaces is related to spectralproperties of symmetrizable operators. Each proper subspace S has a supplement T whichis also a proper subspace.We give a characterization of the compatibility of both subspacesS and T . Several examples are provided that illustrate dierent situations between properand compatible subspaces
publishDate 2015
dc.date.none.fl_str_mv 2015-12
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/11336/18930
Andruchow, Esteban; Chiumiento, Eduardo Hernan; Di Iorio y Lucero, María Eugenia; Proper subspaces and compatibility; Polish Acad Sciences Inst Mathematics; Studia Mathematica; 231; 3; 12-2015; 195-218
0039-3223
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18930
identifier_str_mv Andruchow, Esteban; Chiumiento, Eduardo Hernan; Di Iorio y Lucero, María Eugenia; Proper subspaces and compatibility; Polish Acad Sciences Inst Mathematics; Studia Mathematica; 231; 3; 12-2015; 195-218
0039-3223
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/ 10.4064/sm8225-2-2016
info:eu-repo/semantics/altIdentifier/url/https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/231/3/91441/proper-subspaces-and-compatibility
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1503.00596
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 Polish Acad Sciences Inst Mathematics
publisher.none.fl_str_mv Polish Acad Sciences Inst Mathematics
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 13.070432

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