Geodesic neighborhoods in unitary orbits of self-adjoint operators of K + C

In the present paper, we study the unitary orbit of a compact Hermitian diagonal operator with spectral multiplicity one under the action of the unitary group U(K+C) of the unitization of the compact operators K(H) + C, or equivalently, the quotient U(K+C) /U(D(K+C)) . We relate this and the action...

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Detalles Bibliográficos
Autores: Bottazzi, Tamara Paula, Varela, Alejandro
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/157556
Acceso en línea:http://hdl.handle.net/11336/157556
Access Level:acceso abierto
Palabra clave:UNITARY ORBITS
GEODESIC CURVES
MINIMALITY
FINSLER METRICS
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Geodesic neighborhoods in unitary orbits of self-adjoint operators of K + CBottazzi, Tamara PaulaVarela, AlejandroUNITARY ORBITSGEODESIC CURVESMINIMALITYFINSLER METRICShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In the present paper, we study the unitary orbit of a compact Hermitian diagonal operator with spectral multiplicity one under the action of the unitary group U(K+C) of the unitization of the compact operators K(H) + C, or equivalently, the quotient U(K+C) /U(D(K+C)) . We relate this and the action of different unitary subgroups to describe metric geodesics (using a natural distance) which join end points. As a consequence we obtain a local Hopf-Rinow theorem. We also explore cases about the uniqueness of short curves and prove that there exist some of these that cannot be parameterized using minimal anti-Hermitian operators of K(H) + C.Fil: Bottazzi, Tamara Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Universidad Nacional de Río Negro. Sede Andina. Laboratorio de Procesamiento de Señales Aplicadas y Computación de Alto Rendimiento; ArgentinaFil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaElsevier Science2021-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/157556Bottazzi, Tamara Paula; Varela, Alejandro; Geodesic neighborhoods in unitary orbits of self-adjoint operators of K + C; Elsevier Science; Differential Geometry and its Applications; 77; 8-2021; 1-150926-2245CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0926224521000620info:eu-repo/semantics/altIdentifier/doi/10.1016/j.difgeo.2021.101778info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1904.03650info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T14:05:53Zoai:ri.conicet.gov.ar:11336/157556instacron: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:34982024-05-08 14:05:53.478CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Geodesic neighborhoods in unitary orbits of self-adjoint operators of K + C
title Geodesic neighborhoods in unitary orbits of self-adjoint operators of K + C
spellingShingle Geodesic neighborhoods in unitary orbits of self-adjoint operators of K + C
Bottazzi, Tamara Paula
UNITARY ORBITS
GEODESIC CURVES
MINIMALITY
FINSLER METRICS
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Geodesic neighborhoods in unitary orbits of self-adjoint operators of K + C
title_full Geodesic neighborhoods in unitary orbits of self-adjoint operators of K + C
title_fullStr Geodesic neighborhoods in unitary orbits of self-adjoint operators of K + C
title_full_unstemmed Geodesic neighborhoods in unitary orbits of self-adjoint operators of K + C
title_sort Geodesic neighborhoods in unitary orbits of self-adjoint operators of K + C
dc.creator.none.fl_str_mv Bottazzi, Tamara Paula
Varela, Alejandro
author Bottazzi, Tamara Paula
author_facet Bottazzi, Tamara Paula
Varela, Alejandro
author_role author
author2 Varela, Alejandro
author2_role author
dc.subject.none.fl_str_mv UNITARY ORBITS
GEODESIC CURVES
MINIMALITY
FINSLER METRICS
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic UNITARY ORBITS
GEODESIC CURVES
MINIMALITY
FINSLER METRICS
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description In the present paper, we study the unitary orbit of a compact Hermitian diagonal operator with spectral multiplicity one under the action of the unitary group U(K+C) of the unitization of the compact operators K(H) + C, or equivalently, the quotient U(K+C) /U(D(K+C)) . We relate this and the action of different unitary subgroups to describe metric geodesics (using a natural distance) which join end points. As a consequence we obtain a local Hopf-Rinow theorem. We also explore cases about the uniqueness of short curves and prove that there exist some of these that cannot be parameterized using minimal anti-Hermitian operators of K(H) + C.
publishDate 2021
dc.date.none.fl_str_mv 2021-08
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/11336/157556
Bottazzi, Tamara Paula; Varela, Alejandro; Geodesic neighborhoods in unitary orbits of self-adjoint operators of K + C; Elsevier Science; Differential Geometry and its Applications; 77; 8-2021; 1-15
0926-2245
CONICET Digital
CONICET
url http://hdl.handle.net/11336/157556
identifier_str_mv Bottazzi, Tamara Paula; Varela, Alejandro; Geodesic neighborhoods in unitary orbits of self-adjoint operators of K + C; Elsevier Science; Differential Geometry and its Applications; 77; 8-2021; 1-15
0926-2245
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0926224521000620
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.difgeo.2021.101778
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1904.03650
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15.812429

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