Geometry of ℑ-Stiefel manifolds
- Autores
- Chiumiento, Eduardo Hernán
- Año de publicación
- 2010
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Let ℑ be a separable Banach ideal in the space of bounded operators acting in a Hilbert space ℋ and U(ℋ) ℑ the Banach-Lie group of unitary operators which are perturbations of the identity by elements in ℑ. In this paper we study the geometry of the unitary orbits {UV : U ε U(ℋ) ℑ} and {UVW * : U,W ε U(ℋ) ℑ}, where V is a partial isometry. We give a spatial characterization of these orbits. It turns out that both are included in V + ℑ, and while the first one consists of partial isometries with the same kernel of V , the second is given by partial isometries such that their initial projections and V *V have null index as a pair of projections. We prove that they are smooth submanifolds of the affine Banach space V + ℑ and homogeneous reductive spaces of U(ℋ) ℑ and U(ℋ) ℑ ×U(ℋ) ℑ respectively. Then we endow these orbits with two equivalent Finsler metrics, one provided by the ambient norm of the ideal and the other given by the Banach quotient norm of the Lie algebra of U(ℋ) ℑ (or U(ℋ) ℑ × U(ℋ)I) by the Lie algebra of the isotropy group of the natural actions. We show that they are complete metric spaces with the geodesic distance of these metrics.
Facultad de Ciencias Exactas - Materia
-
Matemática
Banach ideal
Finsler metric
Partial isometry - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by-nc-sa/4.0/
- Repositorio
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/82501
Ver los metadatos del registro completo
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Geometry of ℑ-Stiefel manifoldsChiumiento, Eduardo HernánMatemáticaBanach idealFinsler metricPartial isometryLet ℑ be a separable Banach ideal in the space of bounded operators acting in a Hilbert space ℋ and U(ℋ) ℑ the Banach-Lie group of unitary operators which are perturbations of the identity by elements in ℑ. In this paper we study the geometry of the unitary orbits {UV : U ε U(ℋ) ℑ} and {UVW * : U,W ε U(ℋ) ℑ}, where V is a partial isometry. We give a spatial characterization of these orbits. It turns out that both are included in V + ℑ, and while the first one consists of partial isometries with the same kernel of V , the second is given by partial isometries such that their initial projections and V *V have null index as a pair of projections. We prove that they are smooth submanifolds of the affine Banach space V + ℑ and homogeneous reductive spaces of U(ℋ) ℑ and U(ℋ) ℑ ×U(ℋ) ℑ respectively. Then we endow these orbits with two equivalent Finsler metrics, one provided by the ambient norm of the ideal and the other given by the Banach quotient norm of the Lie algebra of U(ℋ) ℑ (or U(ℋ) ℑ × U(ℋ)I) by the Lie algebra of the isotropy group of the natural actions. We show that they are complete metric spaces with the geodesic distance of these metrics.Facultad de Ciencias Exactas2010info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf341-353http://sedici.unlp.edu.ar/handle/10915/82501enginfo:eu-repo/semantics/altIdentifier/issn/0002-9939info:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9939-09-10080-1info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:15:31Zoai:sedici.unlp.edu.ar:10915/82501Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:15:32.18SEDICI (UNLP) - Universidad Nacional de La Platafalse |
dc.title.none.fl_str_mv |
Geometry of ℑ-Stiefel manifolds |
title |
Geometry of ℑ-Stiefel manifolds |
spellingShingle |
Geometry of ℑ-Stiefel manifolds Chiumiento, Eduardo Hernán Matemática Banach ideal Finsler metric Partial isometry |
title_short |
Geometry of ℑ-Stiefel manifolds |
title_full |
Geometry of ℑ-Stiefel manifolds |
title_fullStr |
Geometry of ℑ-Stiefel manifolds |
title_full_unstemmed |
Geometry of ℑ-Stiefel manifolds |
title_sort |
Geometry of ℑ-Stiefel manifolds |
dc.creator.none.fl_str_mv |
Chiumiento, Eduardo Hernán |
author |
Chiumiento, Eduardo Hernán |
author_facet |
Chiumiento, Eduardo Hernán |
author_role |
author |
dc.subject.none.fl_str_mv |
Matemática Banach ideal Finsler metric Partial isometry |
topic |
Matemática Banach ideal Finsler metric Partial isometry |
dc.description.none.fl_txt_mv |
Let ℑ be a separable Banach ideal in the space of bounded operators acting in a Hilbert space ℋ and U(ℋ) ℑ the Banach-Lie group of unitary operators which are perturbations of the identity by elements in ℑ. In this paper we study the geometry of the unitary orbits {UV : U ε U(ℋ) ℑ} and {UVW * : U,W ε U(ℋ) ℑ}, where V is a partial isometry. We give a spatial characterization of these orbits. It turns out that both are included in V + ℑ, and while the first one consists of partial isometries with the same kernel of V , the second is given by partial isometries such that their initial projections and V *V have null index as a pair of projections. We prove that they are smooth submanifolds of the affine Banach space V + ℑ and homogeneous reductive spaces of U(ℋ) ℑ and U(ℋ) ℑ ×U(ℋ) ℑ respectively. Then we endow these orbits with two equivalent Finsler metrics, one provided by the ambient norm of the ideal and the other given by the Banach quotient norm of the Lie algebra of U(ℋ) ℑ (or U(ℋ) ℑ × U(ℋ)I) by the Lie algebra of the isotropy group of the natural actions. We show that they are complete metric spaces with the geodesic distance of these metrics. Facultad de Ciencias Exactas |
description |
Let ℑ be a separable Banach ideal in the space of bounded operators acting in a Hilbert space ℋ and U(ℋ) ℑ the Banach-Lie group of unitary operators which are perturbations of the identity by elements in ℑ. In this paper we study the geometry of the unitary orbits {UV : U ε U(ℋ) ℑ} and {UVW * : U,W ε U(ℋ) ℑ}, where V is a partial isometry. We give a spatial characterization of these orbits. It turns out that both are included in V + ℑ, and while the first one consists of partial isometries with the same kernel of V , the second is given by partial isometries such that their initial projections and V *V have null index as a pair of projections. We prove that they are smooth submanifolds of the affine Banach space V + ℑ and homogeneous reductive spaces of U(ℋ) ℑ and U(ℋ) ℑ ×U(ℋ) ℑ respectively. Then we endow these orbits with two equivalent Finsler metrics, one provided by the ambient norm of the ideal and the other given by the Banach quotient norm of the Lie algebra of U(ℋ) ℑ (or U(ℋ) ℑ × U(ℋ)I) by the Lie algebra of the isotropy group of the natural actions. We show that they are complete metric spaces with the geodesic distance of these metrics. |
publishDate |
2010 |
dc.date.none.fl_str_mv |
2010 |
dc.type.none.fl_str_mv |
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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article |
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publishedVersion |
dc.identifier.none.fl_str_mv |
http://sedici.unlp.edu.ar/handle/10915/82501 |
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http://sedici.unlp.edu.ar/handle/10915/82501 |
dc.language.none.fl_str_mv |
eng |
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eng |
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info:eu-repo/semantics/altIdentifier/issn/0002-9939 info:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9939-09-10080-1 |
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info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
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openAccess |
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http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
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application/pdf 341-353 |
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