Quotient p-Schatten metrics on spheres

Autores
Andruchow, Esteban; Antunez, Andrea
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let S(H) be the unit sphere of a Hilbert space H and Up(H) thegroup of unitary operators in H such that u−1 belongs to the p-Schatten idealBp(H). This group acts smoothly and transitively in S(H) and endows it witha natural Finsler metric induced by the p-norm kzkp = tr(zz∗)p/21/p. Thismetric is given bykvkx,p = min{kz − ykp : y ∈ gx},where z ∈ Bp(H)ah satisfies that (dπx)1(z) = z · x = v and gx denotes theLie algebra of the subgroup of unitaries which fix x. We call z a lifting of v.A lifting z0 is called a minimal lifting if additionally kvkx,p = kz0kp. Inthis paper we show properties of minimal liftings and we treat the problemof finding short curves α such that α(0) = x and ˙α(0) = v with x ∈ S(H)and v ∈ TxS(H) given. Also we consider the problem of finding short curveswhich join two given endpoints x, y ∈ S(H).
Fil: Andruchow, Esteban. 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; Argentina
Fil: Antunez, Andrea. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Materia
Sphere
Schatten ideals
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/49832
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Quotient p-Schatten metrics on spheresAndruchow, EstebanAntunez, AndreaSphereSchatten idealshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let S(H) be the unit sphere of a Hilbert space H and Up(H) thegroup of unitary operators in H such that u−1 belongs to the p-Schatten idealBp(H). This group acts smoothly and transitively in S(H) and endows it witha natural Finsler metric induced by the p-norm kzkp = tr(zz∗)p/21/p. Thismetric is given bykvkx,p = min{kz − ykp : y ∈ gx},where z ∈ Bp(H)ah satisfies that (dπx)1(z) = z · x = v and gx denotes theLie algebra of the subgroup of unitaries which fix x. We call z a lifting of v.A lifting z0 is called a minimal lifting if additionally kvkx,p = kz0kp. Inthis paper we show properties of minimal liftings and we treat the problemof finding short curves α such that α(0) = x and ˙α(0) = v with x ∈ S(H)and v ∈ TxS(H) given. Also we consider the problem of finding short curveswhich join two given endpoints x, y ∈ S(H).Fil: Andruchow, Esteban. 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; ArgentinaFil: Antunez, Andrea. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaUnión Matemática Argentina2017-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/49832Andruchow, Esteban; Antunez, Andrea; Quotient p-Schatten metrics on spheres; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 58; 1; 4-2017; 21-360041-69321669-9637CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/pdf/v58n1/v58n1a02.pdfinfo:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/revuma.php?p=toc/vol58info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:39:22Zoai:ri.conicet.gov.ar:11336/49832instacron: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:34982025-11-12 09:39:22.713CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Quotient p-Schatten metrics on spheres
title Quotient p-Schatten metrics on spheres
spellingShingle Quotient p-Schatten metrics on spheres
Andruchow, Esteban
Sphere
Schatten ideals
title_short Quotient p-Schatten metrics on spheres
title_full Quotient p-Schatten metrics on spheres
title_fullStr Quotient p-Schatten metrics on spheres
title_full_unstemmed Quotient p-Schatten metrics on spheres
title_sort Quotient p-Schatten metrics on spheres
dc.creator.none.fl_str_mv Andruchow, Esteban
Antunez, Andrea
author Andruchow, Esteban
author_facet Andruchow, Esteban
Antunez, Andrea
author_role author
author2 Antunez, Andrea
author2_role author
dc.subject.none.fl_str_mv Sphere
Schatten ideals
topic Sphere
Schatten ideals
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 S(H) be the unit sphere of a Hilbert space H and Up(H) thegroup of unitary operators in H such that u−1 belongs to the p-Schatten idealBp(H). This group acts smoothly and transitively in S(H) and endows it witha natural Finsler metric induced by the p-norm kzkp = tr(zz∗)p/21/p. Thismetric is given bykvkx,p = min{kz − ykp : y ∈ gx},where z ∈ Bp(H)ah satisfies that (dπx)1(z) = z · x = v and gx denotes theLie algebra of the subgroup of unitaries which fix x. We call z a lifting of v.A lifting z0 is called a minimal lifting if additionally kvkx,p = kz0kp. Inthis paper we show properties of minimal liftings and we treat the problemof finding short curves α such that α(0) = x and ˙α(0) = v with x ∈ S(H)and v ∈ TxS(H) given. Also we consider the problem of finding short curveswhich join two given endpoints x, y ∈ S(H).
Fil: Andruchow, Esteban. 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; Argentina
Fil: Antunez, Andrea. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
description Let S(H) be the unit sphere of a Hilbert space H and Up(H) thegroup of unitary operators in H such that u−1 belongs to the p-Schatten idealBp(H). This group acts smoothly and transitively in S(H) and endows it witha natural Finsler metric induced by the p-norm kzkp = tr(zz∗)p/21/p. Thismetric is given bykvkx,p = min{kz − ykp : y ∈ gx},where z ∈ Bp(H)ah satisfies that (dπx)1(z) = z · x = v and gx denotes theLie algebra of the subgroup of unitaries which fix x. We call z a lifting of v.A lifting z0 is called a minimal lifting if additionally kvkx,p = kz0kp. Inthis paper we show properties of minimal liftings and we treat the problemof finding short curves α such that α(0) = x and ˙α(0) = v with x ∈ S(H)and v ∈ TxS(H) given. Also we consider the problem of finding short curveswhich join two given endpoints x, y ∈ S(H).
publishDate 2017
dc.date.none.fl_str_mv 2017-04
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/11336/49832
Andruchow, Esteban; Antunez, Andrea; Quotient p-Schatten metrics on spheres; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 58; 1; 4-2017; 21-36
0041-6932
1669-9637
CONICET Digital
CONICET
url http://hdl.handle.net/11336/49832
identifier_str_mv Andruchow, Esteban; Antunez, Andrea; Quotient p-Schatten metrics on spheres; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 58; 1; 4-2017; 21-36
0041-6932
1669-9637
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/pdf/v58n1/v58n1a02.pdf
info:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/revuma.php?p=toc/vol58
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Unión Matemática Argentina
publisher.none.fl_str_mv Unión Matemática Argentina
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 12.976206

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