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)$. Given two positive invertible operators P, Q ∈ L(H) and k ∈ (-2,2], we show that N(PTQ^{-1} +P^{-1}TQ + kT) (2+k) N(T), T ∈ I. This extends Zhang's inequality for matrices. We prove that this inequality is equivalent to two particular cases of itself, namely P=Q and Q=P^{-1}. We also characterize those numbers k such that the map ϒ : L(H)→ L(H) given by ϒ (T) = PTQ^{-1} +P^{-1}TQ + kT is invertible, and we estimate the induced norm of ϒ^{-1} acting on the norm ideal I. We compute sharp constants for the involved inequalities in several particular cases.
Fil: Cano, Cristina. Universidad Nacional del Comahue; Argentina
Fil: Mosconi, Irene. Universidad Nacional del Comahue; Argentina
Fil: Stojanoff, Demetrio. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina - Materia
-
POSITIVE MATRICES
INEQUALITIES
UNITARILY INVARIANT NORM - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/106776
Ver los metadatos del registro completo
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Some operator inequalities for unitary invariant normsCano, CristinaMosconi, IreneStojanoff, DemetrioPOSITIVE MATRICESINEQUALITIESUNITARILY INVARIANT NORMhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let L(H) be the algebra of bounded operators on a complex separable Hilbert space H. Let N be a unitary invariant norm defined on a norm ideal I ⊆ L(H)$. 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 Técnicas2025-09-03T09:50:47Zoai: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:34982025-09-03 09:50:48.116CONICET 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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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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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13.13397 |