Some refinements of the Cauchy-Schwarz inequality via orthogonal projections

Autores
Aljawi, Salma; Conde, Cristian Marcelo; Feki, Kais
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we present several refinements of the operator Cauchy-Schwarz inequality for positive operators. Our main result strengthens the classical form of this inequality and serves as a foundation for deriving a series of new inequalities that both generalize and improve upon existing results in the literature. Furthermore, we investigate substantial improvements to the Cauchy–Schwarz inequality by employing orthogonal projections, leading to sharper bounds in various settings. Additionally, we obtain a new perspective on the Cauchy–Schwarz inequality by showing that both the inner product and the product of norms can be characterized as extremal values of projection-dependent expressions. Several related inequalities are also established, many of which recover or extend recent contributions by other authors.
Fil: Aljawi, Salma. Princess Nourah Bint Abdulrahman University; Arabia Saudita
Fil: Conde, Cristian Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Area de Matematica (area de Matematica) ; Instituto de Ciencias ; Universidad Nacional de General Sarmiento;
Fil: Feki, Kais. Najran University; Arabia Saudita
Materia
Cauchy-Schwarz inequality
Positive operators
Orthogonal projections
Selberg’s inequality
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:11336/277176
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/277176
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Some refinements of the Cauchy-Schwarz inequality via orthogonal projectionsAljawi, SalmaConde, Cristian MarceloFeki, KaisCauchy-Schwarz inequalityPositive operatorsOrthogonal projectionsSelberg’s inequalityhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we present several refinements of the operator Cauchy-Schwarz inequality for positive operators. Our main result strengthens the classical form of this inequality and serves as a foundation for deriving a series of new inequalities that both generalize and improve upon existing results in the literature. Furthermore, we investigate substantial improvements to the Cauchy–Schwarz inequality by employing orthogonal projections, leading to sharper bounds in various settings. Additionally, we obtain a new perspective on the Cauchy–Schwarz inequality by showing that both the inner product and the product of norms can be characterized as extremal values of projection-dependent expressions. Several related inequalities are also established, many of which recover or extend recent contributions by other authors.Fil: Aljawi, Salma. Princess Nourah Bint Abdulrahman University; Arabia SauditaFil: Conde, Cristian Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Area de Matematica (area de Matematica) ; Instituto de Ciencias ; Universidad Nacional de General Sarmiento;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/11336/277176Aljawi, Salma; Conde, Cristian Marcelo; Feki, Kais; Some refinements of the Cauchy-Schwarz inequality via orthogonal projections; AIMS Press; AIMS Mathematics; 10; 9; 9-2025; 20294-203112473-6988CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.aimspress.com/article/doi/10.3934/math.2025907info:eu-repo/semantics/altIdentifier/doi/10.3934/math.2025907info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-12-23T14:29:06Zoai:ri.conicet.gov.ar:11336/277176instacron: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:34982025-12-23 14:29:06.57CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Some refinements of the Cauchy-Schwarz inequality via orthogonal projections
title Some refinements of the Cauchy-Schwarz inequality via orthogonal projections
spellingShingle Some refinements of the Cauchy-Schwarz inequality via orthogonal projections
Aljawi, Salma
Cauchy-Schwarz inequality
Positive operators
Orthogonal projections
Selberg’s inequality
title_short Some refinements of the Cauchy-Schwarz inequality via orthogonal projections
title_full Some refinements of the Cauchy-Schwarz inequality via orthogonal projections
title_fullStr Some refinements of the Cauchy-Schwarz inequality via orthogonal projections
title_full_unstemmed Some refinements of the Cauchy-Schwarz inequality via orthogonal projections
title_sort Some refinements of the Cauchy-Schwarz inequality via orthogonal projections
dc.creator.none.fl_str_mv Aljawi, Salma
Conde, Cristian Marcelo
Feki, Kais
author Aljawi, Salma
author_facet Aljawi, Salma
Conde, Cristian Marcelo
Feki, Kais
author_role author
author2 Conde, Cristian Marcelo
Feki, Kais
author2_role author
author
dc.subject.none.fl_str_mv Cauchy-Schwarz inequality
Positive operators
Orthogonal projections
Selberg’s inequality
topic Cauchy-Schwarz inequality
Positive operators
Orthogonal projections
Selberg’s inequality
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper, we present several refinements of the operator Cauchy-Schwarz inequality for positive operators. Our main result strengthens the classical form of this inequality and serves as a foundation for deriving a series of new inequalities that both generalize and improve upon existing results in the literature. Furthermore, we investigate substantial improvements to the Cauchy–Schwarz inequality by employing orthogonal projections, leading to sharper bounds in various settings. Additionally, we obtain a new perspective on the Cauchy–Schwarz inequality by showing that both the inner product and the product of norms can be characterized as extremal values of projection-dependent expressions. Several related inequalities are also established, many of which recover or extend recent contributions by other authors.
Fil: Aljawi, Salma. Princess Nourah Bint Abdulrahman University; Arabia Saudita
Fil: Conde, Cristian Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Area de Matematica (area de Matematica) ; Instituto de Ciencias ; Universidad Nacional de General Sarmiento;
Fil: Feki, Kais. Najran University; Arabia Saudita
description In this paper, we present several refinements of the operator Cauchy-Schwarz inequality for positive operators. Our main result strengthens the classical form of this inequality and serves as a foundation for deriving a series of new inequalities that both generalize and improve upon existing results in the literature. Furthermore, we investigate substantial improvements to the Cauchy–Schwarz inequality by employing orthogonal projections, leading to sharper bounds in various settings. Additionally, we obtain a new perspective on the Cauchy–Schwarz inequality by showing that both the inner product and the product of norms can be characterized as extremal values of projection-dependent expressions. Several related inequalities are also established, many of which recover or extend recent contributions by other authors.
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/11336/277176
Aljawi, Salma; Conde, Cristian Marcelo; Feki, Kais; Some refinements of the Cauchy-Schwarz inequality via orthogonal projections; AIMS Press; AIMS Mathematics; 10; 9; 9-2025; 20294-20311
2473-6988
CONICET Digital
CONICET
url http://hdl.handle.net/11336/277176
identifier_str_mv Aljawi, Salma; Conde, Cristian Marcelo; Feki, Kais; Some refinements of the Cauchy-Schwarz inequality via orthogonal projections; AIMS Press; AIMS Mathematics; 10; 9; 9-2025; 20294-20311
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.2025907
info:eu-repo/semantics/altIdentifier/doi/10.3934/math.2025907
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_ 1852335683187769344
score 12.952241

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