A note about the norm of the sum and the anticommutator of two orthogonal projections
- Autores
- Conde, Cristian Marcelo
- Año de publicación
- 2022
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Revista con referato
Fil: Conde, Cristian Marcelo. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Conde, Cristian Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática Alberto Calderón; Argentina.
En esta nota, demostramos que, para dos proyecciones ortogonales cualesquiera PT,PS sobre un Hilbert, las conocidas fórmulas normativas ?PT+PS?=1+?PTPS?, a menos que PT=PS=0 y ?PTPS+PSPT?=?PTPS?2+?PTPS?, pueden derivarse entre sí. Este resultado se obtiene a partir de la relación entre los espectros de la suma y el producto de dos idempotentes cualesquiera en un álgebra de Banach. Se presentan aplicaciones de nuestros resultados.
In this note, we prove that for any two orthogonal projections PT,PS on a Hilbert the well-known norm formulas ?PT+PS?=1+?PTPS?, unless PT=PS=0 and ?PTPS+PSPT?=?PTPS?2+?PTPS?, can be derived from each other. Such result is obtained from the relation between the spectra of the sum and product of any two idempotents in a Banach algebra. Applications of our results are given. - Fuente
- Journal of Mathematical Analysis and Applications. Ene-2022; 505(2): 1-11
https://www.sciencedirect.com/journal/journal-of-mathematical-analysis-and-applications/vol/505/issue/2 - Materia
-
Orthogonal Projection
Norm Inequalities
Commutator
Anticommutator
Proyección ortogonal
Desigualdades normativas
Matemáticas
Matemática Pura - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-nd/4.0/
- Repositorio
- Institución
- Universidad Nacional de General Sarmiento
- OAI Identificador
- oai:repositorio.ungs.edu.ar:UNGS/2328
Ver los metadatos del registro completo
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A note about the norm of the sum and the anticommutator of two orthogonal projectionsConde, Cristian MarceloOrthogonal ProjectionNorm InequalitiesCommutatorAnticommutatorProyección ortogonalDesigualdades normativasMatemáticasMatemática PuraRevista con referatoFil: Conde, Cristian Marcelo. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.Fil: Conde, Cristian Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática Alberto Calderón; Argentina.En esta nota, demostramos que, para dos proyecciones ortogonales cualesquiera PT,PS sobre un Hilbert, las conocidas fórmulas normativas ?PT+PS?=1+?PTPS?, a menos que PT=PS=0 y ?PTPS+PSPT?=?PTPS?2+?PTPS?, pueden derivarse entre sí. Este resultado se obtiene a partir de la relación entre los espectros de la suma y el producto de dos idempotentes cualesquiera en un álgebra de Banach. Se presentan aplicaciones de nuestros resultados.In this note, we prove that for any two orthogonal projections PT,PS on a Hilbert the well-known norm formulas ?PT+PS?=1+?PTPS?, unless PT=PS=0 and ?PTPS+PSPT?=?PTPS?2+?PTPS?, can be derived from each other. Such result is obtained from the relation between the spectra of the sum and product of any two idempotents in a Banach algebra. Applications of our results are given.Elsevier Science2025-07-24T18:00:32Z2025-07-24T18:00:32Z2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfConde, C. M. (2022). A note about the norm of the sum and the anticommutator of two orthogonal projections. Journal of Mathematical Analysis and Applications, 505(2), 1-11.0022-247Xhttp://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/2328Journal of Mathematical Analysis and Applications. Ene-2022; 505(2): 1-11https://www.sciencedirect.com/journal/journal-of-mathematical-analysis-and-applications/vol/505/issue/2reponame:Repositorio Institucional UNGSinstname:Universidad Nacional de General Sarmientoenghttp://dx.doi.org/10.1016/j.jmaa.2021.125650info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/4.0/2025-10-23T11:20:21Zoai:repositorio.ungs.edu.ar:UNGS/2328instacron:UNGSInstitucionalhttp://repositorio.ungs.edu.ar:8080/Universidad públicahttps://www.ungs.edu.ar/http://repositorio.ungs.edu.ar:8080/oaiubyd@campus.ungs.edu.arArgentinaopendoar:2025-10-23 11:20:21.933Repositorio Institucional UNGS - Universidad Nacional de General Sarmientofalse |
| dc.title.none.fl_str_mv |
A note about the norm of the sum and the anticommutator of two orthogonal projections |
| title |
A note about the norm of the sum and the anticommutator of two orthogonal projections |
| spellingShingle |
A note about the norm of the sum and the anticommutator of two orthogonal projections Conde, Cristian Marcelo Orthogonal Projection Norm Inequalities Commutator Anticommutator Proyección ortogonal Desigualdades normativas Matemáticas Matemática Pura |
| title_short |
A note about the norm of the sum and the anticommutator of two orthogonal projections |
| title_full |
A note about the norm of the sum and the anticommutator of two orthogonal projections |
| title_fullStr |
A note about the norm of the sum and the anticommutator of two orthogonal projections |
| title_full_unstemmed |
A note about the norm of the sum and the anticommutator of two orthogonal projections |
| title_sort |
A note about the norm of the sum and the anticommutator of two orthogonal projections |
| dc.creator.none.fl_str_mv |
Conde, Cristian Marcelo |
| author |
Conde, Cristian Marcelo |
| author_facet |
Conde, Cristian Marcelo |
| author_role |
author |
| dc.subject.none.fl_str_mv |
Orthogonal Projection Norm Inequalities Commutator Anticommutator Proyección ortogonal Desigualdades normativas Matemáticas Matemática Pura |
| topic |
Orthogonal Projection Norm Inequalities Commutator Anticommutator Proyección ortogonal Desigualdades normativas Matemáticas Matemática Pura |
| dc.description.none.fl_txt_mv |
Revista con referato Fil: Conde, Cristian Marcelo. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Fil: Conde, Cristian Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática Alberto Calderón; Argentina. En esta nota, demostramos que, para dos proyecciones ortogonales cualesquiera PT,PS sobre un Hilbert, las conocidas fórmulas normativas ?PT+PS?=1+?PTPS?, a menos que PT=PS=0 y ?PTPS+PSPT?=?PTPS?2+?PTPS?, pueden derivarse entre sí. Este resultado se obtiene a partir de la relación entre los espectros de la suma y el producto de dos idempotentes cualesquiera en un álgebra de Banach. Se presentan aplicaciones de nuestros resultados. In this note, we prove that for any two orthogonal projections PT,PS on a Hilbert the well-known norm formulas ?PT+PS?=1+?PTPS?, unless PT=PS=0 and ?PTPS+PSPT?=?PTPS?2+?PTPS?, can be derived from each other. Such result is obtained from the relation between the spectra of the sum and product of any two idempotents in a Banach algebra. Applications of our results are given. |
| description |
Revista con referato |
| publishDate |
2022 |
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2022 2025-07-24T18:00:32Z 2025-07-24T18:00:32Z |
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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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Conde, C. M. (2022). A note about the norm of the sum and the anticommutator of two orthogonal projections. Journal of Mathematical Analysis and Applications, 505(2), 1-11. 0022-247X http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/2328 |
| identifier_str_mv |
Conde, C. M. (2022). A note about the norm of the sum and the anticommutator of two orthogonal projections. Journal of Mathematical Analysis and Applications, 505(2), 1-11. 0022-247X |
| url |
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/2328 |
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eng |
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eng |
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http://dx.doi.org/10.1016/j.jmaa.2021.125650 |
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info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
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https://creativecommons.org/licenses/by-nc-nd/4.0/ |
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application/pdf application/pdf |
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Elsevier Science |
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Elsevier Science |
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Journal of Mathematical Analysis and Applications. Ene-2022; 505(2): 1-11 https://www.sciencedirect.com/journal/journal-of-mathematical-analysis-and-applications/vol/505/issue/2 reponame:Repositorio Institucional UNGS instname:Universidad Nacional de General Sarmiento |
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Universidad Nacional de General Sarmiento |
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