Some operator inequalities for unitary invariant norms

Autores
Cano, Cristina; Mosconi, Irene; Stojanoff, Demetrio
Año de publicación
2005
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let L(H) be the algebra of bounded operators on a complex separable Hilbert space H.  Let N be a unitary invariant norm  defined on a norm ideal I ⊆ L(H)$. Given two positive invertible operators P, Q ∈ L(H) and k ∈ (-2,2], we show that N(PTQ^{-1} +P^{-1}TQ + kT) (2+k) N(T), T ∈ I. This extends Zhang's inequality for matrices. We prove that this inequality is equivalent to two particular cases of  itself, namely P=Q and Q=P^{-1}. We also characterize  those numbers k such that the map  ϒ : L(H)→ L(H) given by ϒ (T) = PTQ^{-1} +P^{-1}TQ + kT is invertible, and we estimate the induced norm of ϒ^{-1}  acting on the norm ideal I. We compute sharp constants for the involved inequalities in several particular cases.
Fil: Cano, Cristina. Universidad Nacional del Comahue; Argentina
Fil: Mosconi, Irene. Universidad Nacional del Comahue; Argentina
Fil: Stojanoff, Demetrio. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
POSITIVE MATRICES
INEQUALITIES
UNITARILY INVARIANT NORM
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/106776
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/106776
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Some operator inequalities for unitary invariant normsCano, CristinaMosconi, IreneStojanoff, DemetrioPOSITIVE MATRICESINEQUALITIESUNITARILY INVARIANT NORMhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let L(H) be the algebra of bounded operators on a complex separable Hilbert space H.  Let N be a unitary invariant norm  defined on a norm ideal I ⊆ L(H)$. Given two positive invertible operators P, Q ∈ L(H) and k ∈ (-2,2], we show that N(PTQ^{-1} +P^{-1}TQ + kT) (2+k) N(T), T ∈ I. This extends Zhang's inequality for matrices. We prove that this inequality is equivalent to two particular cases of  itself, namely P=Q and Q=P^{-1}. We also characterize  those numbers k such that the map  ϒ : L(H)→ L(H) given by ϒ (T) = PTQ^{-1} +P^{-1}TQ + kT is invertible, and we estimate the induced norm of ϒ^{-1}  acting on the norm ideal I. We compute sharp constants for the involved inequalities in several particular cases.Fil: Cano, Cristina. Universidad Nacional del Comahue; ArgentinaFil: Mosconi, Irene. Universidad Nacional del Comahue; ArgentinaFil: Stojanoff, Demetrio. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaUnión Matemática Argentina2005-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/106776Cano, Cristina; Mosconi, Irene; Stojanoff, Demetrio; Some operator inequalities for unitary invariant norms; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 46; 2; 12-2005; 53-660041-69321669-9637CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://inmabb.criba.edu.ar/revuma/revuma.php?p=toc/vol46info:eu-repo/semantics/altIdentifier/url/https://inmabb.criba.edu.ar/revuma/pdf/v46n1/v46n1a06.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:39:48Zoai:ri.conicet.gov.ar:11336/106776instacron: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:34982025-11-12 09:39:48.59CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Some operator inequalities for unitary invariant norms
title Some operator inequalities for unitary invariant norms
spellingShingle Some operator inequalities for unitary invariant norms
Cano, Cristina
POSITIVE MATRICES
INEQUALITIES
UNITARILY INVARIANT NORM
title_short Some operator inequalities for unitary invariant norms
title_full Some operator inequalities for unitary invariant norms
title_fullStr Some operator inequalities for unitary invariant norms
title_full_unstemmed Some operator inequalities for unitary invariant norms
title_sort Some operator inequalities for unitary invariant norms
dc.creator.none.fl_str_mv Cano, Cristina
Mosconi, Irene
Stojanoff, Demetrio
author Cano, Cristina
author_facet Cano, Cristina
Mosconi, Irene
Stojanoff, Demetrio
author_role author
author2 Mosconi, Irene
Stojanoff, Demetrio
author2_role author
author
dc.subject.none.fl_str_mv POSITIVE MATRICES
INEQUALITIES
UNITARILY INVARIANT NORM
topic POSITIVE MATRICES
INEQUALITIES
UNITARILY INVARIANT NORM
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 L(H) be the algebra of bounded operators on a complex separable Hilbert space H.  Let N be a unitary invariant norm  defined on a norm ideal I ⊆ L(H)$. Given two positive invertible operators P, Q ∈ L(H) and k ∈ (-2,2], we show that N(PTQ^{-1} +P^{-1}TQ + kT) (2+k) N(T), T ∈ I. This extends Zhang's inequality for matrices. We prove that this inequality is equivalent to two particular cases of  itself, namely P=Q and Q=P^{-1}. We also characterize  those numbers k such that the map  ϒ : L(H)→ L(H) given by ϒ (T) = PTQ^{-1} +P^{-1}TQ + kT is invertible, and we estimate the induced norm of ϒ^{-1}  acting on the norm ideal I. We compute sharp constants for the involved inequalities in several particular cases.
Fil: Cano, Cristina. Universidad Nacional del Comahue; Argentina
Fil: Mosconi, Irene. Universidad Nacional del Comahue; Argentina
Fil: Stojanoff, Demetrio. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description Let L(H) be the algebra of bounded operators on a complex separable Hilbert space H.  Let N be a unitary invariant norm  defined on a norm ideal I ⊆ L(H)$. Given two positive invertible operators P, Q ∈ L(H) and k ∈ (-2,2], we show that N(PTQ^{-1} +P^{-1}TQ + kT) (2+k) N(T), T ∈ I. This extends Zhang's inequality for matrices. We prove that this inequality is equivalent to two particular cases of  itself, namely P=Q and Q=P^{-1}. We also characterize  those numbers k such that the map  ϒ : L(H)→ L(H) given by ϒ (T) = PTQ^{-1} +P^{-1}TQ + kT is invertible, and we estimate the induced norm of ϒ^{-1}  acting on the norm ideal I. We compute sharp constants for the involved inequalities in several particular cases.
publishDate 2005
dc.date.none.fl_str_mv 2005-12
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/11336/106776
Cano, Cristina; Mosconi, Irene; Stojanoff, Demetrio; Some operator inequalities for unitary invariant norms; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 46; 2; 12-2005; 53-66
0041-6932
1669-9637
CONICET Digital
CONICET
url http://hdl.handle.net/11336/106776
identifier_str_mv Cano, Cristina; Mosconi, Irene; Stojanoff, Demetrio; Some operator inequalities for unitary invariant norms; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 46; 2; 12-2005; 53-66
0041-6932
1669-9637
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://inmabb.criba.edu.ar/revuma/revuma.php?p=toc/vol46
info:eu-repo/semantics/altIdentifier/url/https://inmabb.criba.edu.ar/revuma/pdf/v46n1/v46n1a06.pdf
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Unión Matemática Argentina
publisher.none.fl_str_mv Unión Matemática Argentina
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
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score 12.976206

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