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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/84728
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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:UNLP2025-10-15T11:08:12Zoai: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:13292025-10-15 11:08:12.796SEDICI (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) |
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openAccess |
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http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
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application/pdf 503-517 |
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