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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/49832
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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 Técnicas2025-09-03T09:50:22Zoai: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:34982025-09-03 09:50:22.446CONICET 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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