Geometry of unitary orbits of pinching operators

Autores
Di Iorio y Lucero, María Eugenia; Chiumiento, Eduardo Hernan
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let I I be a symmetrically-normed ideal of the space of bounded operators acting on a Hilbert space H H . Let View the MathML source {pi}w1 (1≤w≤∞) (1≤w≤∞) be a family of mutually orthogonal projections on H H . The pinching operator associated with the former family of projections is given by P:I⟶I,P(x)=∑wi=1pixpi. Let UI UI denote the Banach–Lie group of the unitary operators whose difference with the identity belongs to I I . We study geometric properties of the orbit UI(P)={LuPLu∗:u∈UI}, UI(P)={LuPLu∗:u∈UI}, where Lu Lu is the left representation of UI UI on the algebra B(I) 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.
Fil: Di Iorio y Lucero, María Eugenia. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
Fil: Chiumiento, Eduardo Hernan. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
Materia
Pinching Operator
Left Representation
Symmetrically Normed Ideal
Submanifold
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/3371
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/3371
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Geometry of unitary orbits of pinching operatorsDi Iorio y Lucero, María EugeniaChiumiento, Eduardo HernanPinching OperatorLeft RepresentationSymmetrically Normed IdealSubmanifoldhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let I I be a symmetrically-normed ideal of the space of bounded operators acting on a Hilbert space H H . Let View the MathML source {pi}w1 (1≤w≤∞) (1≤w≤∞) be a family of mutually orthogonal projections on H H . The pinching operator associated with the former family of projections is given by P:I⟶I,P(x)=∑wi=1pixpi. Let UI UI denote the Banach–Lie group of the unitary operators whose difference with the identity belongs to I I . We study geometric properties of the orbit UI(P)={LuPLu∗:u∈UI}, UI(P)={LuPLu∗:u∈UI}, where Lu Lu is the left representation of UI UI on the algebra B(I) 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.Fil: Di Iorio y Lucero, María Eugenia. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; ArgentinaFil: Chiumiento, Eduardo Hernan. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; ArgentinaAcademic Press Inc Elsevier Science2013-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/3371Di Iorio y Lucero, María Eugenia; Chiumiento, Eduardo Hernan; Geometry of unitary orbits of pinching operators; Academic Press Inc Elsevier Science; Journal Of Mathematical Analysis And Applications; 402; 6-2013; 103-1180022-247Xenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022247X12010517info:eu-repo/semantics/altIdentifier/doi/info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2012.12.060info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:08:44Zoai:ri.conicet.gov.ar:11336/3371instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 12:08:44.359CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Geometry of unitary orbits of pinching operators
title Geometry of unitary orbits of pinching operators
spellingShingle Geometry of unitary orbits of pinching operators
Di Iorio y Lucero, María Eugenia
Pinching Operator
Left Representation
Symmetrically Normed Ideal
Submanifold
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
dc.creator.none.fl_str_mv Di Iorio y Lucero, María Eugenia
Chiumiento, Eduardo Hernan
author Di Iorio y Lucero, María Eugenia
author_facet Di Iorio y Lucero, María Eugenia
Chiumiento, Eduardo Hernan
author_role author
author2 Chiumiento, Eduardo Hernan
author2_role author
dc.subject.none.fl_str_mv Pinching Operator
Left Representation
Symmetrically Normed Ideal
Submanifold
topic Pinching Operator
Left Representation
Symmetrically Normed Ideal
Submanifold
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let I I be a symmetrically-normed ideal of the space of bounded operators acting on a Hilbert space H H . Let View the MathML source {pi}w1 (1≤w≤∞) (1≤w≤∞) be a family of mutually orthogonal projections on H H . The pinching operator associated with the former family of projections is given by P:I⟶I,P(x)=∑wi=1pixpi. Let UI UI denote the Banach–Lie group of the unitary operators whose difference with the identity belongs to I I . We study geometric properties of the orbit UI(P)={LuPLu∗:u∈UI}, UI(P)={LuPLu∗:u∈UI}, where Lu Lu is the left representation of UI UI on the algebra B(I) 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.
Fil: Di Iorio y Lucero, María Eugenia. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
Fil: Chiumiento, Eduardo Hernan. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
description Let I I be a symmetrically-normed ideal of the space of bounded operators acting on a Hilbert space H H . Let View the MathML source {pi}w1 (1≤w≤∞) (1≤w≤∞) be a family of mutually orthogonal projections on H H . The pinching operator associated with the former family of projections is given by P:I⟶I,P(x)=∑wi=1pixpi. Let UI UI denote the Banach–Lie group of the unitary operators whose difference with the identity belongs to I I . We study geometric properties of the orbit UI(P)={LuPLu∗:u∈UI}, UI(P)={LuPLu∗:u∈UI}, where Lu Lu is the left representation of UI UI on the algebra B(I) 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.
publishDate 2013
dc.date.none.fl_str_mv 2013-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/3371
Di Iorio y Lucero, María Eugenia; Chiumiento, Eduardo Hernan; Geometry of unitary orbits of pinching operators; Academic Press Inc Elsevier Science; Journal Of Mathematical Analysis And Applications; 402; 6-2013; 103-118
0022-247X
url http://hdl.handle.net/11336/3371
identifier_str_mv Di Iorio y Lucero, María Eugenia; Chiumiento, Eduardo Hernan; Geometry of unitary orbits of pinching operators; Academic Press Inc Elsevier Science; Journal Of Mathematical Analysis And Applications; 402; 6-2013; 103-118
0022-247X
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022247X12010517
info:eu-repo/semantics/altIdentifier/doi/
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2012.12.060
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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