Quotient p-Schatten metrics on spheres
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
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Unión Matemática Argentina
2024
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I71-R177-UNGS-18092024-12-23T13:21:48Z Quotient p-Schatten metrics on spheres Andruchow, Esteban Antúnez, Andrea C. Sphere Schatten ideals Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina. Fil: Antunez, Andrea. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. 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 (d?x)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 ? such that ?(0) = x and ??(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). 2024-12-23T13:21:48Z 2024-12-23T13:21:48Z 2017 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion Andruchow, E. y Antunez, A. (2017). Quotient p-Schatten metrics on sphere. Revista de la Unión Matemática Argentina, 58(1), 21-36. 0041-6932 http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1809 eng info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf application/pdf Unión Matemática Argentina Revista de la Unión Matemática Argentina. Abr. 2017; 58(1): 21-36 https://inmabb.criba.edu.ar/revuma/revuma.php?p=toc/vol58 |
institution |
Universidad Nacional de General Sarmiento |
institution_str |
I-71 |
repository_str |
R-177 |
collection |
Repositorio Institucional Digital de Acceso Abierto (UNGS) |
language |
Inglés |
orig_language_str_mv |
eng |
topic |
Sphere Schatten ideals |
spellingShingle |
Sphere Schatten ideals Andruchow, Esteban Antúnez, Andrea C. Quotient p-Schatten metrics on spheres |
topic_facet |
Sphere Schatten ideals |
description |
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. |
format |
Artículo Artículo publishedVersion |
author |
Andruchow, Esteban Antúnez, Andrea C. |
author_facet |
Andruchow, Esteban Antúnez, Andrea C. |
author_sort |
Andruchow, Esteban |
title |
Quotient p-Schatten metrics on spheres |
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 |
publisher |
Unión Matemática Argentina |
publishDate |
2024 |
url |
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1809 |
work_keys_str_mv |
AT andruchowesteban quotientpschattenmetricsonspheres AT antunezandreac quotientpschattenmetricsonspheres |
_version_ |
1824528742302613504 |