New Results on Idempotent Operators in Hilbert Spaces

Autores
Aljawi, Salma; Conde, Cristian Marcelo; Feki, Kais; Furuichi, Shigeru
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper provides a new proof of the operator norm identity ∥Q∥ = ∥I −Q∥, where Q is abounded idempotent operator on a complex Hilbert space, and I is the identity operator. Wealso derive explicit lower and upper bounds for the distance from an arbitrary idempotentoperator to the set of orthogonal projections. Our approach simplifies existing proofs.
Fil: Aljawi, Salma. Princess Nourah Bint Abdulrahman University; Arabia Saudita
Fil: Conde, Cristian Marcelo. Area de Matematica (area de Matematica) ; Instituto de Ciencias ; Universidad Nacional de General Sarmiento; . Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Feki, Kais. Najran University; Arabia Saudita
Fil: Furuichi, Shigeru. Nihon University; Japón
Materia
idempotent operators
operator norm
orthogonal projections
oblique projections
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/274695
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/274695
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling New Results on Idempotent Operators in Hilbert SpacesAljawi, SalmaConde, Cristian MarceloFeki, KaisFuruichi, Shigeruidempotent operatorsoperator normorthogonal projectionsoblique projectionshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This paper provides a new proof of the operator norm identity ∥Q∥ = ∥I −Q∥, where Q is abounded idempotent operator on a complex Hilbert space, and I is the identity operator. Wealso derive explicit lower and upper bounds for the distance from an arbitrary idempotentoperator to the set of orthogonal projections. Our approach simplifies existing proofs.Fil: Aljawi, Salma. Princess Nourah Bint Abdulrahman University; Arabia SauditaFil: Conde, Cristian Marcelo. Area de Matematica (area de Matematica) ; Instituto de Ciencias ; Universidad Nacional de General Sarmiento; . Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Feki, Kais. Najran University; Arabia SauditaFil: Furuichi, Shigeru. Nihon University; JapónMultidisciplinary Digital Publishing Institute2025-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/274695Aljawi, Salma; Conde, Cristian Marcelo; Feki, Kais; Furuichi, Shigeru; New Results on Idempotent Operators in Hilbert Spaces; Multidisciplinary Digital Publishing Institute; Axioms; 14; 7; 6-2025; 1-182075-1680CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/2075-1680/14/7/509info:eu-repo/semantics/altIdentifier/doi/10.3390/axioms14070509info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:35:25Zoai:ri.conicet.gov.ar:11336/274695instacron: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:34982025-11-05 10:35:25.697CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv New Results on Idempotent Operators in Hilbert Spaces
title New Results on Idempotent Operators in Hilbert Spaces
spellingShingle New Results on Idempotent Operators in Hilbert Spaces
Aljawi, Salma
idempotent operators
operator norm
orthogonal projections
oblique projections
title_short New Results on Idempotent Operators in Hilbert Spaces
title_full New Results on Idempotent Operators in Hilbert Spaces
title_fullStr New Results on Idempotent Operators in Hilbert Spaces
title_full_unstemmed New Results on Idempotent Operators in Hilbert Spaces
title_sort New Results on Idempotent Operators in Hilbert Spaces
dc.creator.none.fl_str_mv Aljawi, Salma
Conde, Cristian Marcelo
Feki, Kais
Furuichi, Shigeru
author Aljawi, Salma
author_facet Aljawi, Salma
Conde, Cristian Marcelo
Feki, Kais
Furuichi, Shigeru
author_role author
author2 Conde, Cristian Marcelo
Feki, Kais
Furuichi, Shigeru
author2_role author
author
author
dc.subject.none.fl_str_mv idempotent operators
operator norm
orthogonal projections
oblique projections
topic idempotent operators
operator norm
orthogonal projections
oblique projections
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This paper provides a new proof of the operator norm identity ∥Q∥ = ∥I −Q∥, where Q is abounded idempotent operator on a complex Hilbert space, and I is the identity operator. Wealso derive explicit lower and upper bounds for the distance from an arbitrary idempotentoperator to the set of orthogonal projections. Our approach simplifies existing proofs.
Fil: Aljawi, Salma. Princess Nourah Bint Abdulrahman University; Arabia Saudita
Fil: Conde, Cristian Marcelo. Area de Matematica (area de Matematica) ; Instituto de Ciencias ; Universidad Nacional de General Sarmiento; . Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Feki, Kais. Najran University; Arabia Saudita
Fil: Furuichi, Shigeru. Nihon University; Japón
description This paper provides a new proof of the operator norm identity ∥Q∥ = ∥I −Q∥, where Q is abounded idempotent operator on a complex Hilbert space, and I is the identity operator. Wealso derive explicit lower and upper bounds for the distance from an arbitrary idempotentoperator to the set of orthogonal projections. Our approach simplifies existing proofs.
publishDate 2025
dc.date.none.fl_str_mv 2025-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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://hdl.handle.net/11336/274695
Aljawi, Salma; Conde, Cristian Marcelo; Feki, Kais; Furuichi, Shigeru; New Results on Idempotent Operators in Hilbert Spaces; Multidisciplinary Digital Publishing Institute; Axioms; 14; 7; 6-2025; 1-18
2075-1680
CONICET Digital
CONICET
url http://hdl.handle.net/11336/274695
identifier_str_mv Aljawi, Salma; Conde, Cristian Marcelo; Feki, Kais; Furuichi, Shigeru; New Results on Idempotent Operators in Hilbert Spaces; Multidisciplinary Digital Publishing Institute; Axioms; 14; 7; 6-2025; 1-18
2075-1680
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/2075-1680/14/7/509
info:eu-repo/semantics/altIdentifier/doi/10.3390/axioms14070509
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute
publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1847978040717475840
score 13.087074

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