Some operator inequalities for unitarily 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 unitarily invariant norm defined on a norm ideal J ⊆ L(H). Given two positive invertible operators P,Q ∊ L(H) and k ∊ (−2, 2], we show that N (PTQ−1 + P−1TQ + kT) ≥ (2 + k)N(T), T ∊ J. 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 γ : L(H) → L(H) given by γ(T) = PTQ−1 +P−1TQ+kT is invertible, and we estimate the induced norm of γ−1 acting on the norm ideal J. We compute sharp constants for the involved inequalities in several particular cases.
Universidad del Comahue
Facultad de Ciencias Exactas - Materia
-
Matemática
positive matrices
inequalities
unitarily invariant norm - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by/4.0/
- Repositorio
.jpg)
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/156335
Ver los metadatos del registro completo
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Some operator inequalities for unitarily invariant normsCano, CristinaMosconi, IreneStojanoff, DemetrioMatemáticapositive matricesinequalitiesunitarily invariant normLet L(H) be the algebra of bounded operators on a complex separable Hilbert space H. Let N be a unitarily invariant norm defined on a norm ideal J ⊆ L(H). Given two positive invertible operators P,Q ∊ L(H) and k ∊ (−2, 2], we show that N (PTQ−1 + P−1TQ + kT) ≥ (2 + k)N(T), T ∊ J. 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 γ : L(H) → L(H) given by γ(T) = PTQ−1 +P−1TQ+kT is invertible, and we estimate the induced norm of γ−1 acting on the norm ideal J. We compute sharp constants for the involved inequalities in several particular cases.Universidad del ComahueFacultad de Ciencias Exactas2005info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf53-66http://sedici.unlp.edu.ar/handle/10915/156335enginfo:eu-repo/semantics/altIdentifier/issn/1669-9637info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-22T17:21:32Zoai:sedici.unlp.edu.ar:10915/156335Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-22 17:21:32.761SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| dc.title.none.fl_str_mv |
Some operator inequalities for unitarily invariant norms |
| title |
Some operator inequalities for unitarily invariant norms |
| spellingShingle |
Some operator inequalities for unitarily invariant norms Cano, Cristina Matemática positive matrices inequalities unitarily invariant norm |
| title_short |
Some operator inequalities for unitarily invariant norms |
| title_full |
Some operator inequalities for unitarily invariant norms |
| title_fullStr |
Some operator inequalities for unitarily invariant norms |
| title_full_unstemmed |
Some operator inequalities for unitarily invariant norms |
| title_sort |
Some operator inequalities for unitarily 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 |
Matemática positive matrices inequalities unitarily invariant norm |
| topic |
Matemática positive matrices inequalities unitarily invariant norm |
| 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 unitarily invariant norm defined on a norm ideal J ⊆ L(H). Given two positive invertible operators P,Q ∊ L(H) and k ∊ (−2, 2], we show that N (PTQ−1 + P−1TQ + kT) ≥ (2 + k)N(T), T ∊ J. 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 γ : L(H) → L(H) given by γ(T) = PTQ−1 +P−1TQ+kT is invertible, and we estimate the induced norm of γ−1 acting on the norm ideal J. We compute sharp constants for the involved inequalities in several particular cases. Universidad del Comahue Facultad de Ciencias Exactas |
| description |
Let L(H) be the algebra of bounded operators on a complex separable Hilbert space H. Let N be a unitarily invariant norm defined on a norm ideal J ⊆ L(H). Given two positive invertible operators P,Q ∊ L(H) and k ∊ (−2, 2], we show that N (PTQ−1 + P−1TQ + kT) ≥ (2 + k)N(T), T ∊ J. 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 γ : L(H) → L(H) given by γ(T) = PTQ−1 +P−1TQ+kT is invertible, and we estimate the induced norm of γ−1 acting on the norm ideal J. We compute sharp constants for the involved inequalities in several particular cases. |
| publishDate |
2005 |
| dc.date.none.fl_str_mv |
2005 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Articulo http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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eng |
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openAccess |
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