Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices

Autores
Massey, Pedro Gustavo
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let A ⊆ Mn(C) be a unital ∗-subalgebra of the algebra Mn(C) of all n×n complex matrices and let B be an hermitian matrix. Let Un(B) denote the unitary orbit of B in Mn(C) and let EA denote the trace preserving conditional expectation onto A. We give a spectral characterization of the set EA(Un(B)) = {EA(U ∗B U) : U ∈ Mn(C), unitary matrix}. We obtain a similar result for the contractive orbit of a positive semi-definite matrix B. We then use these results to extend the notions of majorization and submajorization between self-adjoint matrices to spectral relations that come together with extended (non-commutative) Schur-Horn type theorems.
Fil: Massey, Pedro Gustavo. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Materia
Extended majorization
non-commutative Schur-Horn theorems
diagonal block compressions
partial traces
unitary orbit
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:11336/19430
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/19430
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Non-commutative Schur-Horn theorems and extended majorization for Hermitian matricesMassey, Pedro GustavoExtended majorizationnon-commutative Schur-Horn theoremsdiagonal block compressionspartial tracesunitary orbithttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let A ⊆ Mn(C) be a unital ∗-subalgebra of the algebra Mn(C) of all n×n complex matrices and let B be an hermitian matrix. Let Un(B) denote the unitary orbit of B in Mn(C) and let EA denote the trace preserving conditional expectation onto A. We give a spectral characterization of the set EA(Un(B)) = {EA(U ∗B U) : U ∈ Mn(C), unitary matrix}. We obtain a similar result for the contractive orbit of a positive semi-definite matrix B. We then use these results to extend the notions of majorization and submajorization between self-adjoint matrices to spectral relations that come together with extended (non-commutative) Schur-Horn type theorems.Fil: Massey, Pedro Gustavo. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaTaylor & Francis Ltd2010-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19430Massey, Pedro Gustavo; Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices; Taylor & Francis Ltd; Linear And Multilinear Algebra; 58; 4; 6-2010; 465-4800308-1087CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0712.2246info:eu-repo/semantics/altIdentifier/url/http://www.tandfonline.com/doi/abs/10.1080/03081080802677615info:eu-repo/semantics/altIdentifier/doi/10.1080/03081080802677615info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:22:54Zoai:ri.conicet.gov.ar:11336/19430instacron: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 10:22:54.626CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices
title Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices
spellingShingle Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices
Massey, Pedro Gustavo
Extended majorization
non-commutative Schur-Horn theorems
diagonal block compressions
partial traces
unitary orbit
title_short Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices
title_full Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices
title_fullStr Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices
title_full_unstemmed Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices
title_sort Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices
dc.creator.none.fl_str_mv Massey, Pedro Gustavo
author Massey, Pedro Gustavo
author_facet Massey, Pedro Gustavo
author_role author
dc.subject.none.fl_str_mv Extended majorization
non-commutative Schur-Horn theorems
diagonal block compressions
partial traces
unitary orbit
topic Extended majorization
non-commutative Schur-Horn theorems
diagonal block compressions
partial traces
unitary orbit
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 A ⊆ Mn(C) be a unital ∗-subalgebra of the algebra Mn(C) of all n×n complex matrices and let B be an hermitian matrix. Let Un(B) denote the unitary orbit of B in Mn(C) and let EA denote the trace preserving conditional expectation onto A. We give a spectral characterization of the set EA(Un(B)) = {EA(U ∗B U) : U ∈ Mn(C), unitary matrix}. We obtain a similar result for the contractive orbit of a positive semi-definite matrix B. We then use these results to extend the notions of majorization and submajorization between self-adjoint matrices to spectral relations that come together with extended (non-commutative) Schur-Horn type theorems.
Fil: Massey, Pedro Gustavo. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
description Let A ⊆ Mn(C) be a unital ∗-subalgebra of the algebra Mn(C) of all n×n complex matrices and let B be an hermitian matrix. Let Un(B) denote the unitary orbit of B in Mn(C) and let EA denote the trace preserving conditional expectation onto A. We give a spectral characterization of the set EA(Un(B)) = {EA(U ∗B U) : U ∈ Mn(C), unitary matrix}. We obtain a similar result for the contractive orbit of a positive semi-definite matrix B. We then use these results to extend the notions of majorization and submajorization between self-adjoint matrices to spectral relations that come together with extended (non-commutative) Schur-Horn type theorems.
publishDate 2010
dc.date.none.fl_str_mv 2010-06
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/11336/19430
Massey, Pedro Gustavo; Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices; Taylor & Francis Ltd; Linear And Multilinear Algebra; 58; 4; 6-2010; 465-480
0308-1087
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19430
identifier_str_mv Massey, Pedro Gustavo; Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices; Taylor & Francis Ltd; Linear And Multilinear Algebra; 58; 4; 6-2010; 465-480
0308-1087
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://arxiv.org/abs/0712.2246
info:eu-repo/semantics/altIdentifier/url/http://www.tandfonline.com/doi/abs/10.1080/03081080802677615
info:eu-repo/semantics/altIdentifier/doi/10.1080/03081080802677615
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
dc.publisher.none.fl_str_mv Taylor & Francis Ltd
publisher.none.fl_str_mv Taylor & Francis Ltd
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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