Geometry of unitary orbits of pinching operators

Let I be a symmetrically-normed ideal of the space of bounded operators acting on a Hilbert space H. Let {pi}1w(1≤w≤∞) be a family of mutually orthogonal projections on H. The pinching operator associated with the former family of projections is given by P:I→I,P(x)=∑i=1wpixpi. Let UI denote the Bana...

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Detalles Bibliográficos
Autores principales: Chiumiento, Eduardo Hernán, Di Iorio y Lucero, M. E.
Formato: Articulo
Lenguaje:Inglés
Publicado: 2013
Materias:
Matemática
Covering space
Left representation
Pinching operator
Submanifold
Symmetrically-normed ideal
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/85541
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-85541
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Covering space
Left representation
Pinching operator
Submanifold
Symmetrically-normed ideal
spellingShingle Matemática
Covering space
Left representation
Pinching operator
Submanifold
Symmetrically-normed ideal
Chiumiento, Eduardo Hernán
Di Iorio y Lucero, M. E.
Geometry of unitary orbits of pinching operators
topic_facet Matemática
Covering space
Left representation
Pinching operator
Submanifold
Symmetrically-normed ideal
description Let I be a symmetrically-normed ideal of the space of bounded operators acting on a Hilbert space H. Let {pi}1w(1≤w≤∞) be a family of mutually orthogonal projections on H. The pinching operator associated with the former family of projections is given by P:I→I,P(x)=∑i=1wpixpi. Let UI denote the Banach-Lie group of the unitary operators whose difference with the identity belongs to I. We study geometric properties of the orbit UI(P)={LuPLu*:u∈UI}, where Lu is the left representation of UI on the algebra B(I) of bounded operators acting on I. The results include necessary and sufficient conditions for UI(P) to be a submanifold of B(I). Special features arise in the case of the ideal K of compact operators. In general, UK(P) turns out to be a non complemented submanifold of B(K). We find a necessary and sufficient condition for UK(P) to have complemented tangent spaces in B(K). We also show that UI(P) is a covering space of another orbit of pinching operators.
format Articulo
Articulo
author Chiumiento, Eduardo Hernán
Di Iorio y Lucero, M. E.
author_facet Chiumiento, Eduardo Hernán
Di Iorio y Lucero, M. E.
author_sort Chiumiento, Eduardo Hernán
title Geometry of unitary orbits of pinching operators
title_short Geometry of unitary orbits of pinching operators
title_full Geometry of unitary orbits of pinching operators
title_fullStr Geometry of unitary orbits of pinching operators
title_full_unstemmed Geometry of unitary orbits of pinching operators
title_sort geometry of unitary orbits of pinching operators
publishDate 2013
url http://sedici.unlp.edu.ar/handle/10915/85541
work_keys_str_mv AT chiumientoeduardohernan geometryofunitaryorbitsofpinchingoperators
AT diiorioylucerome geometryofunitaryorbitsofpinchingoperators
bdutipo_str Repositorios
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