On restricted diagonalization

Autores
Chiumiento, Eduardo Hernan; Massey, Pedro Gustavo
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let H be a separable infinite-dimensional complex Hilbert space, B(H) the algebra of bounded linear operators acting on H and J a proper two-sided ideal of B(H). Denote by UJ(H) the group of all unitary operators of the form I+J. Recall that an operator A∈B(H) is diagonalizable if there exists a unitary operator U such that UAU⁎ is diagonal with respect to some orthonormal basis. A more restrictive notion of diagonalization can be formulated with respect to a fixed orthonormal basis e={en}n≥1 and a proper operator ideal J as follows: A∈B(H) is called restrictedly diagonalizable if there exists U∈UJ(H) such that UAU⁎ is diagonal with respect to e. In this work we give a sufficient condition for a diagonalizable operator to be restrictedly diagonalizable. This condition becomes a characterization when the ideal is arithmetic mean closed. Then we obtain results on the structure of the set of all restrictedly diagonalizable operators. In this way we answer several open problems recently raised by Beltiţă, Patnaik and Weiss.
Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
ESSENTIAL CODIMENSION
OPERATOR IDEAL
RESTRICTED DIAGONALIZATION
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:11336/150672
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling On restricted diagonalizationChiumiento, Eduardo HernanMassey, Pedro GustavoESSENTIAL CODIMENSIONOPERATOR IDEALRESTRICTED DIAGONALIZATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let H be a separable infinite-dimensional complex Hilbert space, B(H) the algebra of bounded linear operators acting on H and J a proper two-sided ideal of B(H). Denote by UJ(H) the group of all unitary operators of the form I+J. Recall that an operator A∈B(H) is diagonalizable if there exists a unitary operator U such that UAU⁎ is diagonal with respect to some orthonormal basis. A more restrictive notion of diagonalization can be formulated with respect to a fixed orthonormal basis e={en}n≥1 and a proper operator ideal J as follows: A∈B(H) is called restrictedly diagonalizable if there exists U∈UJ(H) such that UAU⁎ is diagonal with respect to e. In this work we give a sufficient condition for a diagonalizable operator to be restrictedly diagonalizable. This condition becomes a characterization when the ideal is arithmetic mean closed. Then we obtain results on the structure of the set of all restrictedly diagonalizable operators. In this way we answer several open problems recently raised by Beltiţă, Patnaik and Weiss.Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaAcademic Press Inc Elsevier Science2021-06info: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/11336/150672Chiumiento, Eduardo Hernan; Massey, Pedro Gustavo; On restricted diagonalization; Academic Press Inc Elsevier Science; Journal of Functional Analysis; 282; 4; 6-2021; 1-270022-1236CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0022123621004249?via%3Dihubinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jfa.2021.109342info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2106.06612info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:57:35Zoai:ri.conicet.gov.ar:11336/150672instacron: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:34982025-10-15 14:57:35.601CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On restricted diagonalization
title On restricted diagonalization
spellingShingle On restricted diagonalization
Chiumiento, Eduardo Hernan
ESSENTIAL CODIMENSION
OPERATOR IDEAL
RESTRICTED DIAGONALIZATION
title_short On restricted diagonalization
title_full On restricted diagonalization
title_fullStr On restricted diagonalization
title_full_unstemmed On restricted diagonalization
title_sort On restricted diagonalization
dc.creator.none.fl_str_mv Chiumiento, Eduardo Hernan
Massey, Pedro Gustavo
author Chiumiento, Eduardo Hernan
author_facet Chiumiento, Eduardo Hernan
Massey, Pedro Gustavo
author_role author
author2 Massey, Pedro Gustavo
author2_role author
dc.subject.none.fl_str_mv ESSENTIAL CODIMENSION
OPERATOR IDEAL
RESTRICTED DIAGONALIZATION
topic ESSENTIAL CODIMENSION
OPERATOR IDEAL
RESTRICTED DIAGONALIZATION
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 H be a separable infinite-dimensional complex Hilbert space, B(H) the algebra of bounded linear operators acting on H and J a proper two-sided ideal of B(H). Denote by UJ(H) the group of all unitary operators of the form I+J. Recall that an operator A∈B(H) is diagonalizable if there exists a unitary operator U such that UAU⁎ is diagonal with respect to some orthonormal basis. A more restrictive notion of diagonalization can be formulated with respect to a fixed orthonormal basis e={en}n≥1 and a proper operator ideal J as follows: A∈B(H) is called restrictedly diagonalizable if there exists U∈UJ(H) such that UAU⁎ is diagonal with respect to e. In this work we give a sufficient condition for a diagonalizable operator to be restrictedly diagonalizable. This condition becomes a characterization when the ideal is arithmetic mean closed. Then we obtain results on the structure of the set of all restrictedly diagonalizable operators. In this way we answer several open problems recently raised by Beltiţă, Patnaik and Weiss.
Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description Let H be a separable infinite-dimensional complex Hilbert space, B(H) the algebra of bounded linear operators acting on H and J a proper two-sided ideal of B(H). Denote by UJ(H) the group of all unitary operators of the form I+J. Recall that an operator A∈B(H) is diagonalizable if there exists a unitary operator U such that UAU⁎ is diagonal with respect to some orthonormal basis. A more restrictive notion of diagonalization can be formulated with respect to a fixed orthonormal basis e={en}n≥1 and a proper operator ideal J as follows: A∈B(H) is called restrictedly diagonalizable if there exists U∈UJ(H) such that UAU⁎ is diagonal with respect to e. In this work we give a sufficient condition for a diagonalizable operator to be restrictedly diagonalizable. This condition becomes a characterization when the ideal is arithmetic mean closed. Then we obtain results on the structure of the set of all restrictedly diagonalizable operators. In this way we answer several open problems recently raised by Beltiţă, Patnaik and Weiss.
publishDate 2021
dc.date.none.fl_str_mv 2021-06
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/11336/150672
Chiumiento, Eduardo Hernan; Massey, Pedro Gustavo; On restricted diagonalization; Academic Press Inc Elsevier Science; Journal of Functional Analysis; 282; 4; 6-2021; 1-27
0022-1236
CONICET Digital
CONICET
url http://hdl.handle.net/11336/150672
identifier_str_mv Chiumiento, Eduardo Hernan; Massey, Pedro Gustavo; On restricted diagonalization; Academic Press Inc Elsevier Science; Journal of Functional Analysis; 282; 4; 6-2021; 1-27
0022-1236
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.sciencedirect.com/science/article/abs/pii/S0022123621004249?via%3Dihub
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jfa.2021.109342
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2106.06612
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 13.22299

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