Best approximation by diagonal operators in Schatten ideals
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Elsevier Science Inc
2025
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| Acceso en línea: | http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/2135 |
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I71-R177-UNGS-2135 |
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I71-R177-UNGS-21352025-03-13T17:31:10Z Best approximation by diagonal operators in Schatten ideals Bottazzi, Tamara Paula Minimality Schatten P-Norm Compact Operator Diagonal Operators Orthogonality Matemáticas Matemática Pura Revista con referato Fil: Bottazzi, Tamara Paula. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Fil: Bottazzi, Tamara Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Si X es el conjunto de operadores compactos o p-Schatten sobre un espacio complejo separable de Hilbert H, estudiamos la existencia y propiedades de caracterización del A∈X hermitiano tal que |||A|||≤|||A+D|||,for allD∈D(X) o equivalentemente |||A|||=minD∈D(X)|||A+D|||=dist(A,D(X)), donde D(X) es el subespacio de operadores diagonales de X en cualquier base prefijada de H y |||⋅||| es la norma de operador habitual en cada X. Utilizamos la ortogonalidad de Birkhoff-James como herramienta para caracterizar y desarrollar propiedades de estos operadores en cada contexto. También proporcionamos varios ejemplos ilustrativos. If X is the set of compact or p-Schatten operators over a complex Hilbert separable space H, we study the existence and characterization properties of Hermitian A∈X such that |||A|||≤|||A+D|||,for allD∈D(X) or equivalently |||A|||=minD∈D(X)|||A+D|||=dist(A,D(X)), where D(X) is the subspace of diagonal operators of X in any prefixed basis of H and |||⋅||| is the usual operator norm in each X. We use Birkhoff-James orthogonality as a tool to characterize and develop properties of these operators in each context. We also provide several illustrative examples. Se X é o conjunto de operadores compactos ou p-Schatten sobre um espaço separável de Hilbert complexo H, estudamos a existência e propriedades de caracterização do Hermitiano A∈X tal que |||A|||≤|||A+D|||,para todosD∈D(X) ou equivalentemente |||A|||=minD∈D(X)|||A+D|||=dist(A,D(X)), onde D(X) é o subespaço dos operadores diagonais de X em qualquer base prefixada de H e |||⋅||| é a norma usual do operador em cada X. Utilizamos a ortogonalidade de Birkhoff-James como ferramenta para caracterizar e desenvolver propriedades desses operadores em cada contexto. Também fornecemos vários exemplos ilustrativos. 2025-03-13T17:23:44Z 2025-03-13T17:23:44Z 2021 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion Bottazzi, T. P. (2021). Best approximation by diagonal operators in Schatten ideals. Linear Algebra and its Applications, 620, 1-26. 0024-3795 http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/2135 eng https://doi.org/10.1016/j.laa.2021.02.025 info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf application/pdf Elsevier Science Inc Linear Algebra and its Applications. Jul. 2021; 620: 1-26 https://www.sciencedirect.com/journal/linear-algebra-and-its-applications/vol/620/suppl/C |
| institution |
Universidad Nacional de General Sarmiento |
| institution_str |
I-71 |
| repository_str |
R-177 |
| collection |
Repositorio Institucional Digital de Acceso Abierto (UNGS) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| topic |
Minimality Schatten P-Norm Compact Operator Diagonal Operators Orthogonality Matemáticas Matemática Pura |
| spellingShingle |
Minimality Schatten P-Norm Compact Operator Diagonal Operators Orthogonality Matemáticas Matemática Pura Bottazzi, Tamara Paula Best approximation by diagonal operators in Schatten ideals |
| topic_facet |
Minimality Schatten P-Norm Compact Operator Diagonal Operators Orthogonality Matemáticas Matemática Pura |
| description |
Revista con referato |
| format |
Artículo Artículo publishedVersion |
| author |
Bottazzi, Tamara Paula |
| author_facet |
Bottazzi, Tamara Paula |
| author_sort |
Bottazzi, Tamara Paula |
| title |
Best approximation by diagonal operators in Schatten ideals |
| title_short |
Best approximation by diagonal operators in Schatten ideals |
| title_full |
Best approximation by diagonal operators in Schatten ideals |
| title_fullStr |
Best approximation by diagonal operators in Schatten ideals |
| title_full_unstemmed |
Best approximation by diagonal operators in Schatten ideals |
| title_sort |
best approximation by diagonal operators in schatten ideals |
| publisher |
Elsevier Science Inc |
| publishDate |
2025 |
| url |
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/2135 |
| work_keys_str_mv |
AT bottazzitamarapaula bestapproximationbydiagonaloperatorsinschattenideals |
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1826997429042413568 |