Multivariable Schur-Horn theorems

Autores
Massey, Pedro Gustavo; Ravichandran, Mohan
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove a variety of results describing the diagonals of tuples of commuting hermitian operators in type II 1  1 factors. These results, motivated by work of Arveson and Kadison, are generalizations of the classical Schur-Horn theorem to the infinite-dimensional, multivariable setting. Our description of these possible diagonals uses a natural generalization of the classical notion of majorization. In the special case when both the given tuple and the desired diagonal have finite joint spectrum, our results are complete. When the tuples do not have finite joint spectrum, we are able to prove strong approximate results. Unlike the single variable case, the multivariable case presents several surprises and we point out obstructions to extending our complete description in the finite spectrum case to the general case. We also discuss the problem of characterizing diagonals of commuting tuples in B ( H ) B(H) and give approximate characterizations in this case as well.
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
Fil: Ravichandran, Mohan. Mimar Sinan Fine Arts University; Turquía
Materia
Joint Majorization
Schur-Horn Theorem
Ii_1 Factors
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:11336/18992
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/18992
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network_name_str CONICET Digital (CONICET)
spelling Multivariable Schur-Horn theoremsMassey, Pedro GustavoRavichandran, MohanJoint MajorizationSchur-Horn TheoremIi_1 Factorshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove a variety of results describing the diagonals of tuples of commuting hermitian operators in type II 1  1 factors. These results, motivated by work of Arveson and Kadison, are generalizations of the classical Schur-Horn theorem to the infinite-dimensional, multivariable setting. Our description of these possible diagonals uses a natural generalization of the classical notion of majorization. In the special case when both the given tuple and the desired diagonal have finite joint spectrum, our results are complete. When the tuples do not have finite joint spectrum, we are able to prove strong approximate results. Unlike the single variable case, the multivariable case presents several surprises and we point out obstructions to extending our complete description in the finite spectrum case to the general case. We also discuss the problem of characterizing diagonals of commuting tuples in B ( H ) B(H) and give approximate characterizations in this case as well.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; ArgentinaFil: Ravichandran, Mohan. Mimar Sinan Fine Arts University; TurquíaLondon Mathematical Society2016-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18992Massey, Pedro Gustavo; Ravichandran, Mohan; Multivariable Schur-Horn theorems; London Mathematical Society; Proceedings Of The London Mathematical Society; 112; 1; 2-2016; 206-2340024-6115CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1112/plms/pdv067/fullinfo:eu-repo/semantics/altIdentifier/doi/10.1112/plms/pdv067info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:08:42Zoai:ri.conicet.gov.ar:11336/18992instacron: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:34982025-09-10 13:08:43.005CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Multivariable Schur-Horn theorems
title Multivariable Schur-Horn theorems
spellingShingle Multivariable Schur-Horn theorems
Massey, Pedro Gustavo
Joint Majorization
Schur-Horn Theorem
Ii_1 Factors
title_short Multivariable Schur-Horn theorems
title_full Multivariable Schur-Horn theorems
title_fullStr Multivariable Schur-Horn theorems
title_full_unstemmed Multivariable Schur-Horn theorems
title_sort Multivariable Schur-Horn theorems
dc.creator.none.fl_str_mv Massey, Pedro Gustavo
Ravichandran, Mohan
author Massey, Pedro Gustavo
author_facet Massey, Pedro Gustavo
Ravichandran, Mohan
author_role author
author2 Ravichandran, Mohan
author2_role author
dc.subject.none.fl_str_mv Joint Majorization
Schur-Horn Theorem
Ii_1 Factors
topic Joint Majorization
Schur-Horn Theorem
Ii_1 Factors
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We prove a variety of results describing the diagonals of tuples of commuting hermitian operators in type II 1  1 factors. These results, motivated by work of Arveson and Kadison, are generalizations of the classical Schur-Horn theorem to the infinite-dimensional, multivariable setting. Our description of these possible diagonals uses a natural generalization of the classical notion of majorization. In the special case when both the given tuple and the desired diagonal have finite joint spectrum, our results are complete. When the tuples do not have finite joint spectrum, we are able to prove strong approximate results. Unlike the single variable case, the multivariable case presents several surprises and we point out obstructions to extending our complete description in the finite spectrum case to the general case. We also discuss the problem of characterizing diagonals of commuting tuples in B ( H ) B(H) and give approximate characterizations in this case as well.
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
Fil: Ravichandran, Mohan. Mimar Sinan Fine Arts University; Turquía
description We prove a variety of results describing the diagonals of tuples of commuting hermitian operators in type II 1  1 factors. These results, motivated by work of Arveson and Kadison, are generalizations of the classical Schur-Horn theorem to the infinite-dimensional, multivariable setting. Our description of these possible diagonals uses a natural generalization of the classical notion of majorization. In the special case when both the given tuple and the desired diagonal have finite joint spectrum, our results are complete. When the tuples do not have finite joint spectrum, we are able to prove strong approximate results. Unlike the single variable case, the multivariable case presents several surprises and we point out obstructions to extending our complete description in the finite spectrum case to the general case. We also discuss the problem of characterizing diagonals of commuting tuples in B ( H ) B(H) and give approximate characterizations in this case as well.
publishDate 2016
dc.date.none.fl_str_mv 2016-02
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/11336/18992
Massey, Pedro Gustavo; Ravichandran, Mohan; Multivariable Schur-Horn theorems; London Mathematical Society; Proceedings Of The London Mathematical Society; 112; 1; 2-2016; 206-234
0024-6115
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18992
identifier_str_mv Massey, Pedro Gustavo; Ravichandran, Mohan; Multivariable Schur-Horn theorems; London Mathematical Society; Proceedings Of The London Mathematical Society; 112; 1; 2-2016; 206-234
0024-6115
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1112/plms/pdv067/full
info:eu-repo/semantics/altIdentifier/doi/10.1112/plms/pdv067
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 London Mathematical Society
publisher.none.fl_str_mv London Mathematical Society
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 12.993085

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