Index of Hadamard multiplication by positive matrices II
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...
Guardado en:
| Autores principales: | , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2001
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/84728 |
| Aporte de: |
| id |
I19-R120-10915-84728 |
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| record_format |
dspace |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
| collection |
SEDICI (UNLP) |
| language |
Inglés |
| topic |
Ciencias Exactas Matemática 47A30 47B15 Hadamard product Norm inequalities Positive semidefinite matrices |
| spellingShingle |
Ciencias Exactas Matemática 47A30 47B15 Hadamard product Norm inequalities Positive semidefinite matrices Corach, Gustavo Stojanoff, Demetrio Index of Hadamard multiplication by positive matrices II |
| topic_facet |
Ciencias Exactas Matemática 47A30 47B15 Hadamard product Norm inequalities Positive semidefinite matrices |
| 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. |
| format |
Articulo Articulo |
| author |
Corach, Gustavo Stojanoff, Demetrio |
| author_facet |
Corach, Gustavo Stojanoff, Demetrio |
| author_sort |
Corach, Gustavo |
| title |
Index of Hadamard multiplication by positive matrices II |
| 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 |
| publishDate |
2001 |
| url |
http://sedici.unlp.edu.ar/handle/10915/84728 |
| work_keys_str_mv |
AT corachgustavo indexofhadamardmultiplicationbypositivematricesii AT stojanoffdemetrio indexofhadamardmultiplicationbypositivematricesii |
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Repositorios |
| _version_ |
1764820489143844864 |