Jensen's inequality for spectral order and submajorization

Autores
Antezana, Jorge Abel; Massey, Pedro Gustavo; Stojanoff, Demetrio
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let A be a C*-algebra and φ{symbol} : A → L (H) be a positive unital map. Then, for a convex function f : I → R defined on some open interval and a self-adjoint element a ∈ A whose spectrum lies in I, we obtain a Jensen's-type inequality f (φ{symbol} (a)) ≤ φ{symbol} (f (a)) where ≤ denotes an operator preorder (usual order, spectral preorder, majorization) and depends on the class of convex functions considered, i.e., monotone convex or arbitrary convex functions. Some extensions of Jensen's-type inequalities to the multi-variable case are considered.
Facultad de Ciencias Exactas
Materia
Matemática
Convex functions
Jensen's inequality
Majorization
Positive maps
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/83285
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/83285
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Jensen's inequality for spectral order and submajorizationAntezana, Jorge AbelMassey, Pedro GustavoStojanoff, DemetrioMatemáticaConvex functionsJensen's inequalityMajorizationPositive mapsLet A be a C*-algebra and φ{symbol} : A → L (H) be a positive unital map. Then, for a convex function f : I → R defined on some open interval and a self-adjoint element a ∈ A whose spectrum lies in I, we obtain a Jensen's-type inequality f (φ{symbol} (a)) ≤ φ{symbol} (f (a)) where ≤ denotes an operator preorder (usual order, spectral preorder, majorization) and depends on the class of convex functions considered, i.e., monotone convex or arbitrary convex functions. Some extensions of Jensen's-type inequalities to the multi-variable case are considered.Facultad de Ciencias Exactas2007info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf297-307http://sedici.unlp.edu.ar/handle/10915/83285enginfo:eu-repo/semantics/altIdentifier/issn/0022-247Xinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2006.08.029info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-22T16:56:33Zoai:sedici.unlp.edu.ar:10915/83285Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-22 16:56:33.273SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Jensen's inequality for spectral order and submajorization
title Jensen's inequality for spectral order and submajorization
spellingShingle Jensen's inequality for spectral order and submajorization
Antezana, Jorge Abel
Matemática
Convex functions
Jensen's inequality
Majorization
Positive maps
title_short Jensen's inequality for spectral order and submajorization
title_full Jensen's inequality for spectral order and submajorization
title_fullStr Jensen's inequality for spectral order and submajorization
title_full_unstemmed Jensen's inequality for spectral order and submajorization
title_sort Jensen's inequality for spectral order and submajorization
dc.creator.none.fl_str_mv Antezana, Jorge Abel
Massey, Pedro Gustavo
Stojanoff, Demetrio
author Antezana, Jorge Abel
author_facet Antezana, Jorge Abel
Massey, Pedro Gustavo
Stojanoff, Demetrio
author_role author
author2 Massey, Pedro Gustavo
Stojanoff, Demetrio
author2_role author
author
dc.subject.none.fl_str_mv Matemática
Convex functions
Jensen's inequality
Majorization
Positive maps
topic Matemática
Convex functions
Jensen's inequality
Majorization
Positive maps
dc.description.none.fl_txt_mv Let A be a C*-algebra and φ{symbol} : A → L (H) be a positive unital map. Then, for a convex function f : I → R defined on some open interval and a self-adjoint element a ∈ A whose spectrum lies in I, we obtain a Jensen's-type inequality f (φ{symbol} (a)) ≤ φ{symbol} (f (a)) where ≤ denotes an operator preorder (usual order, spectral preorder, majorization) and depends on the class of convex functions considered, i.e., monotone convex or arbitrary convex functions. Some extensions of Jensen's-type inequalities to the multi-variable case are considered.
Facultad de Ciencias Exactas
description Let A be a C*-algebra and φ{symbol} : A → L (H) be a positive unital map. Then, for a convex function f : I → R defined on some open interval and a self-adjoint element a ∈ A whose spectrum lies in I, we obtain a Jensen's-type inequality f (φ{symbol} (a)) ≤ φ{symbol} (f (a)) where ≤ denotes an operator preorder (usual order, spectral preorder, majorization) and depends on the class of convex functions considered, i.e., monotone convex or arbitrary convex functions. Some extensions of Jensen's-type inequalities to the multi-variable case are considered.
publishDate 2007
dc.date.none.fl_str_mv 2007
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/83285
url http://sedici.unlp.edu.ar/handle/10915/83285
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0022-247X
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2006.08.029
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
297-307
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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score 12.982451

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