Some operator inequalities for unitarily invariant norms
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’...
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| Formato: | Articulo |
| Lenguaje: | Inglés |
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2005
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/156335 |
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I19-R120-10915-1563352023-08-16T04:06:11Z http://sedici.unlp.edu.ar/handle/10915/156335 Some operator inequalities for unitarily invariant norms Cano, Cristina Mosconi, Irene Stojanoff, Demetrio 2005 2023-08-15T14:45:02Z en Matemática positive matrices inequalities unitarily invariant norm 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 Articulo Articulo http://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International (CC BY 4.0) application/pdf 53-66 |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
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SEDICI (UNLP) |
| language |
Inglés |
| topic |
Matemática positive matrices inequalities unitarily invariant norm |
| spellingShingle |
Matemática positive matrices inequalities unitarily invariant norm Cano, Cristina Mosconi, Irene Stojanoff, Demetrio Some operator inequalities for unitarily invariant norms |
| topic_facet |
Matemática positive matrices inequalities unitarily invariant norm |
| 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. |
| format |
Articulo Articulo |
| author |
Cano, Cristina Mosconi, Irene Stojanoff, Demetrio |
| author_facet |
Cano, Cristina Mosconi, Irene Stojanoff, Demetrio |
| author_sort |
Cano, Cristina |
| title |
Some operator inequalities for unitarily invariant norms |
| 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 |
| publishDate |
2005 |
| url |
http://sedici.unlp.edu.ar/handle/10915/156335 |
| work_keys_str_mv |
AT canocristina someoperatorinequalitiesforunitarilyinvariantnorms AT mosconiirene someoperatorinequalitiesforunitarilyinvariantnorms AT stojanoffdemetrio someoperatorinequalitiesforunitarilyinvariantnorms |
| _version_ |
1807220984995905536 |