Characterizations of normaloid operators in Hilbert spaces via Birkhoff–James orthogonality

Autores
Aladsani, Feryal; Alajyan, Asmahan; Conde, Cristian Marcelo; Feki, Kais
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let H be a complex Hilbert space and B(H) the algebra of bounded linear operators on H. An operator T is said to be normaloid if its numerical radius w(T) equals its operator norm kTk. In this paper, we establish several characterizations of normaloid operators in Hilbert spaces. In particular, we investigate these operators through the framework of Birkhoff–James orthogonality and normparallelism. Mainly, we show that T is normaloid if, and only if, there exists ξ0 ∈ C with |ξ0| = kTk such that I ⊥BJ (T − ξ0I), where ⊥BJ denotes Birkhoff–James orthogonality. We also present further equivalent formulations and explore various structural consequences of these characterizations.
Fil: Aladsani, Feryal. King Faisal University; Arabia Saudita
Fil: Alajyan, Asmahan. King Saud University; Arabia Saudita
Fil: Conde, Cristian Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias. Área de Matemática;
Fil: Feki, Kais. Najran University; Arabia Saudita
Materia
Positive operator
Numerical radius
Operator norm
Inequalities
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:11336/275832
Acceder
id CONICETDig_b95fa3c8e0a801c717c4be7e44b77052
oai_identifier_str oai:ri.conicet.gov.ar:11336/275832
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Characterizations of normaloid operators in Hilbert spaces via Birkhoff–James orthogonalityAladsani, FeryalAlajyan, AsmahanConde, Cristian MarceloFeki, KaisPositive operatorNumerical radiusOperator normInequalitieshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let H be a complex Hilbert space and B(H) the algebra of bounded linear operators on H. An operator T is said to be normaloid if its numerical radius w(T) equals its operator norm kTk. In this paper, we establish several characterizations of normaloid operators in Hilbert spaces. In particular, we investigate these operators through the framework of Birkhoff–James orthogonality and normparallelism. Mainly, we show that T is normaloid if, and only if, there exists ξ0 ∈ C with |ξ0| = kTk such that I ⊥BJ (T − ξ0I), where ⊥BJ denotes Birkhoff–James orthogonality. We also present further equivalent formulations and explore various structural consequences of these characterizations.Fil: Aladsani, Feryal. King Faisal University; Arabia SauditaFil: Alajyan, Asmahan. King Saud University; Arabia SauditaFil: Conde, Cristian Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias. Área de Matemática;Fil: Feki, Kais. Najran University; Arabia SauditaAIMS Press2025-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/275832Aladsani, Feryal; Alajyan, Asmahan; Conde, Cristian Marcelo; Feki, Kais; Characterizations of normaloid operators in Hilbert spaces via Birkhoff–James orthogonality; AIMS Press; AIMS Mathematics; 10; 9; 9-2025; 20066-200832473-6988CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.aimspress.com/article/doi/10.3934/math.2025897info:eu-repo/semantics/altIdentifier/doi/10.3934/math.2025897info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-12-03T09:51:45Zoai:ri.conicet.gov.ar:11336/275832instacron: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:34982025-12-03 09:51:45.38CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Characterizations of normaloid operators in Hilbert spaces via Birkhoff–James orthogonality
title Characterizations of normaloid operators in Hilbert spaces via Birkhoff–James orthogonality
spellingShingle Characterizations of normaloid operators in Hilbert spaces via Birkhoff–James orthogonality
Aladsani, Feryal
Positive operator
Numerical radius
Operator norm
Inequalities
title_short Characterizations of normaloid operators in Hilbert spaces via Birkhoff–James orthogonality
title_full Characterizations of normaloid operators in Hilbert spaces via Birkhoff–James orthogonality
title_fullStr Characterizations of normaloid operators in Hilbert spaces via Birkhoff–James orthogonality
title_full_unstemmed Characterizations of normaloid operators in Hilbert spaces via Birkhoff–James orthogonality
title_sort Characterizations of normaloid operators in Hilbert spaces via Birkhoff–James orthogonality
dc.creator.none.fl_str_mv Aladsani, Feryal
Alajyan, Asmahan
Conde, Cristian Marcelo
Feki, Kais
author Aladsani, Feryal
author_facet Aladsani, Feryal
Alajyan, Asmahan
Conde, Cristian Marcelo
Feki, Kais
author_role author
author2 Alajyan, Asmahan
Conde, Cristian Marcelo
Feki, Kais
author2_role author
author
author
dc.subject.none.fl_str_mv Positive operator
Numerical radius
Operator norm
Inequalities
topic Positive operator
Numerical radius
Operator norm
Inequalities
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let H be a complex Hilbert space and B(H) the algebra of bounded linear operators on H. An operator T is said to be normaloid if its numerical radius w(T) equals its operator norm kTk. In this paper, we establish several characterizations of normaloid operators in Hilbert spaces. In particular, we investigate these operators through the framework of Birkhoff–James orthogonality and normparallelism. Mainly, we show that T is normaloid if, and only if, there exists ξ0 ∈ C with |ξ0| = kTk such that I ⊥BJ (T − ξ0I), where ⊥BJ denotes Birkhoff–James orthogonality. We also present further equivalent formulations and explore various structural consequences of these characterizations.
Fil: Aladsani, Feryal. King Faisal University; Arabia Saudita
Fil: Alajyan, Asmahan. King Saud University; Arabia Saudita
Fil: Conde, Cristian Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias. Área de Matemática;
Fil: Feki, Kais. Najran University; Arabia Saudita
description Let H be a complex Hilbert space and B(H) the algebra of bounded linear operators on H. An operator T is said to be normaloid if its numerical radius w(T) equals its operator norm kTk. In this paper, we establish several characterizations of normaloid operators in Hilbert spaces. In particular, we investigate these operators through the framework of Birkhoff–James orthogonality and normparallelism. Mainly, we show that T is normaloid if, and only if, there exists ξ0 ∈ C with |ξ0| = kTk such that I ⊥BJ (T − ξ0I), where ⊥BJ denotes Birkhoff–James orthogonality. We also present further equivalent formulations and explore various structural consequences of these characterizations.
publishDate 2025
dc.date.none.fl_str_mv 2025-09
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/11336/275832
Aladsani, Feryal; Alajyan, Asmahan; Conde, Cristian Marcelo; Feki, Kais; Characterizations of normaloid operators in Hilbert spaces via Birkhoff–James orthogonality; AIMS Press; AIMS Mathematics; 10; 9; 9-2025; 20066-20083
2473-6988
CONICET Digital
CONICET
url http://hdl.handle.net/11336/275832
identifier_str_mv Aladsani, Feryal; Alajyan, Asmahan; Conde, Cristian Marcelo; Feki, Kais; Characterizations of normaloid operators in Hilbert spaces via Birkhoff–James orthogonality; AIMS Press; AIMS Mathematics; 10; 9; 9-2025; 20066-20083
2473-6988
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.aimspress.com/article/doi/10.3934/math.2025897
info:eu-repo/semantics/altIdentifier/doi/10.3934/math.2025897
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 AIMS Press
publisher.none.fl_str_mv AIMS Press
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_ 1850505943471620096
score 13.275514

Publicaciones similares