Index of Hadamard multiplication by positive matrices II

Autores
Corach, Gustavo; Stojanoff, Demetrio
Año de publicación
2001
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
For each n×n positive semidefinite matrix A we define the minimal index I(A)=max{λ≥0:A∘B≥λB for all B≥0} and, for each norm N, the N-index IN(A)=min{N(A∘B):B≥0 and N(B)=1}, where A ∘ B=[aijbij] is the Hadamard or Schur product of A=[aij] and B=[bij] and B≥0 means that B is a positive semidefinite matrix. A comparison between these indexes is done, for different choices of the norm N. As an application we find, for each bounded invertible selfadjoint operator S on a Hilbert space, the best constant M(S) such that ∥STS+S-1TS-1∥≥M(S)∥T∥ for all T≥0.
Facultad de Ciencias Exactas
Materia
Ciencias Exactas
Matemática
47A30
47B15
Hadamard product
Norm inequalities
Positive semidefinite matrices
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:10915/84728

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network_name_str SEDICI (UNLP)
spelling Index of Hadamard multiplication by positive matrices IICorach, GustavoStojanoff, DemetrioCiencias ExactasMatemática47A3047B15Hadamard productNorm inequalitiesPositive semidefinite matricesFor each n×n positive semidefinite matrix A we define the minimal index I(A)=max{λ≥0:A∘B≥λB for all B≥0} and, for each norm N, the N-index I<SUB>N</SUB>(A)=min{N(A∘B):B≥0 and N(B)=1}, where A ∘ B=[a<SUB>ij</SUB>b<SUB>ij</SUB>] is the Hadamard or Schur product of A=[a<SUB>ij</SUB>] and B=[b<SUB>ij</SUB>] and B≥0 means that B is a positive semidefinite matrix. A comparison between these indexes is done, for different choices of the norm N. As an application we find, for each bounded invertible selfadjoint operator S on a Hilbert space, the best constant M(S) such that ∥STS+S<SUP>-1</SUP>TS<SUP>-1</SUP>∥≥M(S)∥T∥ for all T≥0.Facultad de Ciencias Exactas2001info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf503-517http://sedici.unlp.edu.ar/handle/10915/84728enginfo:eu-repo/semantics/altIdentifier/issn/0024-3795info:eu-repo/semantics/altIdentifier/doi/10.1016/S0024-3795(01)00306-8info: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:UNLP2025-10-22T16:57:07Zoai:sedici.unlp.edu.ar:10915/84728Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-22 16:57:07.925SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Index of Hadamard multiplication by positive matrices II
title Index of Hadamard multiplication by positive matrices II
spellingShingle Index of Hadamard multiplication by positive matrices II
Corach, Gustavo
Ciencias Exactas
Matemática
47A30
47B15
Hadamard product
Norm inequalities
Positive semidefinite matrices
title_short Index of Hadamard multiplication by positive matrices II
title_full Index of Hadamard multiplication by positive matrices II
title_fullStr Index of Hadamard multiplication by positive matrices II
title_full_unstemmed Index of Hadamard multiplication by positive matrices II
title_sort Index of Hadamard multiplication by positive matrices II
dc.creator.none.fl_str_mv Corach, Gustavo
Stojanoff, Demetrio
author Corach, Gustavo
author_facet Corach, Gustavo
Stojanoff, Demetrio
author_role author
author2 Stojanoff, Demetrio
author2_role author
dc.subject.none.fl_str_mv Ciencias Exactas
Matemática
47A30
47B15
Hadamard product
Norm inequalities
Positive semidefinite matrices
topic Ciencias Exactas
Matemática
47A30
47B15
Hadamard product
Norm inequalities
Positive semidefinite matrices
dc.description.none.fl_txt_mv For each n×n positive semidefinite matrix A we define the minimal index I(A)=max{λ≥0:A∘B≥λB for all B≥0} and, for each norm N, the N-index I<SUB>N</SUB>(A)=min{N(A∘B):B≥0 and N(B)=1}, where A ∘ B=[a<SUB>ij</SUB>b<SUB>ij</SUB>] is the Hadamard or Schur product of A=[a<SUB>ij</SUB>] and B=[b<SUB>ij</SUB>] and B≥0 means that B is a positive semidefinite matrix. A comparison between these indexes is done, for different choices of the norm N. As an application we find, for each bounded invertible selfadjoint operator S on a Hilbert space, the best constant M(S) such that ∥STS+S<SUP>-1</SUP>TS<SUP>-1</SUP>∥≥M(S)∥T∥ for all T≥0.
Facultad de Ciencias Exactas
description For each n×n positive semidefinite matrix A we define the minimal index I(A)=max{λ≥0:A∘B≥λB for all B≥0} and, for each norm N, the N-index I<SUB>N</SUB>(A)=min{N(A∘B):B≥0 and N(B)=1}, where A ∘ B=[a<SUB>ij</SUB>b<SUB>ij</SUB>] is the Hadamard or Schur product of A=[a<SUB>ij</SUB>] and B=[b<SUB>ij</SUB>] and B≥0 means that B is a positive semidefinite matrix. A comparison between these indexes is done, for different choices of the norm N. As an application we find, for each bounded invertible selfadjoint operator S on a Hilbert space, the best constant M(S) such that ∥STS+S<SUP>-1</SUP>TS<SUP>-1</SUP>∥≥M(S)∥T∥ for all T≥0.
publishDate 2001
dc.date.none.fl_str_mv 2001
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/10915/84728
url http://sedici.unlp.edu.ar/handle/10915/84728
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0024-3795
info:eu-repo/semantics/altIdentifier/doi/10.1016/S0024-3795(01)00306-8
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
503-517
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instname:Universidad Nacional de La Plata
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