The Schur-Horn theorem for operators and frames with prescribed norms and frame operator

Autores
Antezana, Jorge Abel; Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio
Año de publicación
2005
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let H be a Hilbert space. Given a bounded positive definite operator S on H, and a bounded sequence c={c_k}_k∈N of nonnegative real numbers, the pair (S, c) is frame admissible, if there exists a frame {ƒ_k}_k ∈N on H with frame operator S, such that ||ƒ_k||^2=c_k, k ∈ N. We relate the existence of such frames with the Schur-Horn theorem of majorization, and give a reformulation of the extended version of Schur-Horn theorem, due to A. Neumann. We use this to get necessary conditions (and to generalize known sufficient conditions) for a pair (S, c) to be frame admissible.
Fil: Antezana, Jorge Abel. 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
Fil: Ruiz, Mariano Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
Frames
Schur Horn theorem
majorization
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:11336/101034
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The Schur-Horn theorem for operators and frames with prescribed norms and frame operatorAntezana, Jorge AbelMassey, Pedro GustavoRuiz, Mariano AndresStojanoff, DemetrioFramesSchur Horn theoremmajorizationhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let H be a Hilbert space. Given a bounded positive definite operator S on H, and a bounded sequence c={c_k}_k∈N of nonnegative real numbers, the pair (S, c) is frame admissible, if there exists a frame {ƒ_k}_k ∈N on H with frame operator S, such that ||ƒ_k||^2=c_k, k ∈ N. We relate the existence of such frames with the Schur-Horn theorem of majorization, and give a reformulation of the extended version of Schur-Horn theorem, due to A. Neumann. We use this to get necessary conditions (and to generalize known sufficient conditions) for a pair (S, c) to be frame admissible.Fil: Antezana, Jorge Abel. 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; ArgentinaFil: Ruiz, Mariano Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaUniversity of Illinois at Urbana-Champaign2005-10info: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/11336/101034Antezana, Jorge Abel; Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; The Schur-Horn theorem for operators and frames with prescribed norms and frame operator; University of Illinois at Urbana-Champaign; Illinois Journal of Mathematics; 51; 2; 10-2005; 537-5600019-20821945-6581CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.projecteuclid.org/euclid.ijm/1258138415info:eu-repo/semantics/altIdentifier/url/https://www.projecteuclid.org/download/pdf_1/euclid.ijm/1258138428info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/math/0508646info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:41:55Zoai:ri.conicet.gov.ar:11336/101034instacron: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 09:41:56.156CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The Schur-Horn theorem for operators and frames with prescribed norms and frame operator
title The Schur-Horn theorem for operators and frames with prescribed norms and frame operator
spellingShingle The Schur-Horn theorem for operators and frames with prescribed norms and frame operator
Antezana, Jorge Abel
Frames
Schur Horn theorem
majorization
title_short The Schur-Horn theorem for operators and frames with prescribed norms and frame operator
title_full The Schur-Horn theorem for operators and frames with prescribed norms and frame operator
title_fullStr The Schur-Horn theorem for operators and frames with prescribed norms and frame operator
title_full_unstemmed The Schur-Horn theorem for operators and frames with prescribed norms and frame operator
title_sort The Schur-Horn theorem for operators and frames with prescribed norms and frame operator
dc.creator.none.fl_str_mv Antezana, Jorge Abel
Massey, Pedro Gustavo
Ruiz, Mariano Andres
Stojanoff, Demetrio
author Antezana, Jorge Abel
author_facet Antezana, Jorge Abel
Massey, Pedro Gustavo
Ruiz, Mariano Andres
Stojanoff, Demetrio
author_role author
author2 Massey, Pedro Gustavo
Ruiz, Mariano Andres
Stojanoff, Demetrio
author2_role author
author
author
dc.subject.none.fl_str_mv Frames
Schur Horn theorem
majorization
topic Frames
Schur Horn theorem
majorization
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 Hilbert space. Given a bounded positive definite operator S on H, and a bounded sequence c={c_k}_k∈N of nonnegative real numbers, the pair (S, c) is frame admissible, if there exists a frame {ƒ_k}_k ∈N on H with frame operator S, such that ||ƒ_k||^2=c_k, k ∈ N. We relate the existence of such frames with the Schur-Horn theorem of majorization, and give a reformulation of the extended version of Schur-Horn theorem, due to A. Neumann. We use this to get necessary conditions (and to generalize known sufficient conditions) for a pair (S, c) to be frame admissible.
Fil: Antezana, Jorge Abel. 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
Fil: Ruiz, Mariano Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. 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 Hilbert space. Given a bounded positive definite operator S on H, and a bounded sequence c={c_k}_k∈N of nonnegative real numbers, the pair (S, c) is frame admissible, if there exists a frame {ƒ_k}_k ∈N on H with frame operator S, such that ||ƒ_k||^2=c_k, k ∈ N. We relate the existence of such frames with the Schur-Horn theorem of majorization, and give a reformulation of the extended version of Schur-Horn theorem, due to A. Neumann. We use this to get necessary conditions (and to generalize known sufficient conditions) for a pair (S, c) to be frame admissible.
publishDate 2005
dc.date.none.fl_str_mv 2005-10
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/11336/101034
Antezana, Jorge Abel; Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; The Schur-Horn theorem for operators and frames with prescribed norms and frame operator; University of Illinois at Urbana-Champaign; Illinois Journal of Mathematics; 51; 2; 10-2005; 537-560
0019-2082
1945-6581
CONICET Digital
CONICET
url http://hdl.handle.net/11336/101034
identifier_str_mv Antezana, Jorge Abel; Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; The Schur-Horn theorem for operators and frames with prescribed norms and frame operator; University of Illinois at Urbana-Champaign; Illinois Journal of Mathematics; 51; 2; 10-2005; 537-560
0019-2082
1945-6581
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.projecteuclid.org/euclid.ijm/1258138415
info:eu-repo/semantics/altIdentifier/url/https://www.projecteuclid.org/download/pdf_1/euclid.ijm/1258138428
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/math/0508646
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 University of Illinois at Urbana-Champaign
publisher.none.fl_str_mv University of Illinois at Urbana-Champaign
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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