On a conjecture by Mbekhta about best approximation by polar factors
- Autores
- Chiumiento, Eduardo Hernan
- Año de publicación
- 2021
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- The polar factor of a bounded operator acting on a Hilbert space is the unique partial isometry arising in the polar decomposition. It is well known that the polar factor might not be a best approximant to its associated operator in the set of all partial isometries, when the distance is measured in the operator norm. We show that the polar factor of an arbitrary operator T is a best approximant to T in the set of all partial isometries X such that dim(ker(X)∩ker(T)⊥) ≤ dim(ker(X)⊥∩ker(T)). We also provide a characterization of best approximations. This work is motivated by a recent conjecture by M. Mbekhta, which can be answered using our results.
Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina - Materia
-
BEST APPROXIMATION
INDEX
PAIR OF PROJECTIONS
PARTIAL ISOMETRIES
POLAR DECOMPOSITION
POLAR FACTOR - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/150989
Ver los metadatos del registro completo
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On a conjecture by Mbekhta about best approximation by polar factorsChiumiento, Eduardo HernanBEST APPROXIMATIONINDEXPAIR OF PROJECTIONSPARTIAL ISOMETRIESPOLAR DECOMPOSITIONPOLAR FACTORhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The polar factor of a bounded operator acting on a Hilbert space is the unique partial isometry arising in the polar decomposition. It is well known that the polar factor might not be a best approximant to its associated operator in the set of all partial isometries, when the distance is measured in the operator norm. We show that the polar factor of an arbitrary operator T is a best approximant to T in the set of all partial isometries X such that dim(ker(X)∩ker(T)⊥) ≤ dim(ker(X)⊥∩ker(T)). We also provide a characterization of best approximations. This work is motivated by a recent conjecture by M. Mbekhta, which can be answered using our results.Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaAmerican Mathematical Society2021-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/150989Chiumiento, Eduardo Hernan; On a conjecture by Mbekhta about best approximation by polar factors; American Mathematical Society; Proceedings of the American Mathematical Society; 149; 9; 11-2021; 3913-39220002-99391088-6826CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/proc/2021-149-09/S0002-9939-2021-15537-8/info:eu-repo/semantics/altIdentifier/doi/10.1090/proc/15537info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2106.01825info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:28:30Zoai:ri.conicet.gov.ar:11336/150989instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:28:31.176CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
On a conjecture by Mbekhta about best approximation by polar factors |
| title |
On a conjecture by Mbekhta about best approximation by polar factors |
| spellingShingle |
On a conjecture by Mbekhta about best approximation by polar factors Chiumiento, Eduardo Hernan BEST APPROXIMATION INDEX PAIR OF PROJECTIONS PARTIAL ISOMETRIES POLAR DECOMPOSITION POLAR FACTOR |
| title_short |
On a conjecture by Mbekhta about best approximation by polar factors |
| title_full |
On a conjecture by Mbekhta about best approximation by polar factors |
| title_fullStr |
On a conjecture by Mbekhta about best approximation by polar factors |
| title_full_unstemmed |
On a conjecture by Mbekhta about best approximation by polar factors |
| title_sort |
On a conjecture by Mbekhta about best approximation by polar factors |
| dc.creator.none.fl_str_mv |
Chiumiento, Eduardo Hernan |
| author |
Chiumiento, Eduardo Hernan |
| author_facet |
Chiumiento, Eduardo Hernan |
| author_role |
author |
| dc.subject.none.fl_str_mv |
BEST APPROXIMATION INDEX PAIR OF PROJECTIONS PARTIAL ISOMETRIES POLAR DECOMPOSITION POLAR FACTOR |
| topic |
BEST APPROXIMATION INDEX PAIR OF PROJECTIONS PARTIAL ISOMETRIES POLAR DECOMPOSITION POLAR FACTOR |
| purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| dc.description.none.fl_txt_mv |
The polar factor of a bounded operator acting on a Hilbert space is the unique partial isometry arising in the polar decomposition. It is well known that the polar factor might not be a best approximant to its associated operator in the set of all partial isometries, when the distance is measured in the operator norm. We show that the polar factor of an arbitrary operator T is a best approximant to T in the set of all partial isometries X such that dim(ker(X)∩ker(T)⊥) ≤ dim(ker(X)⊥∩ker(T)). We also provide a characterization of best approximations. This work is motivated by a recent conjecture by M. Mbekhta, which can be answered using our results. Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina |
| description |
The polar factor of a bounded operator acting on a Hilbert space is the unique partial isometry arising in the polar decomposition. It is well known that the polar factor might not be a best approximant to its associated operator in the set of all partial isometries, when the distance is measured in the operator norm. We show that the polar factor of an arbitrary operator T is a best approximant to T in the set of all partial isometries X such that dim(ker(X)∩ker(T)⊥) ≤ dim(ker(X)⊥∩ker(T)). We also provide a characterization of best approximations. This work is motivated by a recent conjecture by M. Mbekhta, which can be answered using our results. |
| publishDate |
2021 |
| dc.date.none.fl_str_mv |
2021-11 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
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http://hdl.handle.net/11336/150989 Chiumiento, Eduardo Hernan; On a conjecture by Mbekhta about best approximation by polar factors; American Mathematical Society; Proceedings of the American Mathematical Society; 149; 9; 11-2021; 3913-3922 0002-9939 1088-6826 CONICET Digital CONICET |
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http://hdl.handle.net/11336/150989 |
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Chiumiento, Eduardo Hernan; On a conjecture by Mbekhta about best approximation by polar factors; American Mathematical Society; Proceedings of the American Mathematical Society; 149; 9; 11-2021; 3913-3922 0002-9939 1088-6826 CONICET Digital CONICET |
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eng |
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eng |
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American Mathematical Society |
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American Mathematical Society |
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