Geometry of ℑ-Stiefel manifolds

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...

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Autor principal: Chiumiento, Eduardo Hernán
Formato: Articulo
Lenguaje:Inglés
Publicado: 2010
Materias:
Matemática
Banach ideal
Finsler metric
Partial isometry
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/82501
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-82501
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Banach ideal
Finsler metric
Partial isometry
spellingShingle Matemática
Banach ideal
Finsler metric
Partial isometry
Chiumiento, Eduardo Hernán
Geometry of ℑ-Stiefel manifolds
topic_facet Matemática
Banach ideal
Finsler metric
Partial isometry
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.
format Articulo
Articulo
author Chiumiento, Eduardo Hernán
author_facet Chiumiento, Eduardo Hernán
author_sort Chiumiento, Eduardo Hernán
title Geometry of ℑ-Stiefel manifolds
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
publishDate 2010
url http://sedici.unlp.edu.ar/handle/10915/82501
work_keys_str_mv AT chiumientoeduardohernan geometryofistiefelmanifolds
bdutipo_str Repositorios
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