The iterated Aluthge transforms of a matrix converge

Autores
Antezana, Jorge Abel; Pujals, Enrique R.; Stojanoff, Demetrio
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given an r×r complex matrix T, if T=U|T| is the polar decomposition of T, then, the Aluthge transform is defined by Δ(T)=|T|1/2U|T|1/2. Let Δn(T) denote the n-times iterated Aluthge transform of T, i.e., Δ0(T)=T and Δn(T)=Δ(Δn-1(T)), nεN. We prove that the sequence {Δn(T)}nεN converges for every r×r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003. We also analyze the regularity of the limit function.
Facultad de Ciencias Exactas
Materia
Matemática
Aluthge transform
Polar decomposition
Similarity orbit
Stable manifold theorem
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/84303
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/84303
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling The iterated Aluthge transforms of a matrix convergeAntezana, Jorge AbelPujals, Enrique R.Stojanoff, DemetrioMatemáticaAluthge transformPolar decompositionSimilarity orbitStable manifold theoremGiven an r×r complex matrix T, if T=U|T| is the polar decomposition of T, then, the Aluthge transform is defined by Δ(T)=|T|<sup>1/2</sup>U|T|<sup>1/2</sup>. Let Δ<sup>n</sup>(T) denote the n-times iterated Aluthge transform of T, i.e., Δ<sup>0</sup>(T)=T and Δ<sup>n</sup>(T)=Δ(Δ<sup>n-1</sup>(T)), nεN. We prove that the sequence {Δ<sup>n</sup>(T)}<sub>nεN</sub> converges for every r×r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003. We also analyze the regularity of the limit function.Facultad de Ciencias Exactas2011-01-30info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf1591-1620http://sedici.unlp.edu.ar/handle/10915/84303enginfo:eu-repo/semantics/altIdentifier/issn/0001-8708info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2010.08.012info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-12-23T11:18:19Zoai:sedici.unlp.edu.ar:10915/84303Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-12-23 11:18:19.486SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv The iterated Aluthge transforms of a matrix converge
title The iterated Aluthge transforms of a matrix converge
spellingShingle The iterated Aluthge transforms of a matrix converge
Antezana, Jorge Abel
Matemática
Aluthge transform
Polar decomposition
Similarity orbit
Stable manifold theorem
title_short The iterated Aluthge transforms of a matrix converge
title_full The iterated Aluthge transforms of a matrix converge
title_fullStr The iterated Aluthge transforms of a matrix converge
title_full_unstemmed The iterated Aluthge transforms of a matrix converge
title_sort The iterated Aluthge transforms of a matrix converge
dc.creator.none.fl_str_mv Antezana, Jorge Abel
Pujals, Enrique R.
Stojanoff, Demetrio
author Antezana, Jorge Abel
author_facet Antezana, Jorge Abel
Pujals, Enrique R.
Stojanoff, Demetrio
author_role author
author2 Pujals, Enrique R.
Stojanoff, Demetrio
author2_role author
author
dc.subject.none.fl_str_mv Matemática
Aluthge transform
Polar decomposition
Similarity orbit
Stable manifold theorem
topic Matemática
Aluthge transform
Polar decomposition
Similarity orbit
Stable manifold theorem
dc.description.none.fl_txt_mv Given an r×r complex matrix T, if T=U|T| is the polar decomposition of T, then, the Aluthge transform is defined by Δ(T)=|T|<sup>1/2</sup>U|T|<sup>1/2</sup>. Let Δ<sup>n</sup>(T) denote the n-times iterated Aluthge transform of T, i.e., Δ<sup>0</sup>(T)=T and Δ<sup>n</sup>(T)=Δ(Δ<sup>n-1</sup>(T)), nεN. We prove that the sequence {Δ<sup>n</sup>(T)}<sub>nεN</sub> converges for every r×r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003. We also analyze the regularity of the limit function.
Facultad de Ciencias Exactas
description Given an r×r complex matrix T, if T=U|T| is the polar decomposition of T, then, the Aluthge transform is defined by Δ(T)=|T|<sup>1/2</sup>U|T|<sup>1/2</sup>. Let Δ<sup>n</sup>(T) denote the n-times iterated Aluthge transform of T, i.e., Δ<sup>0</sup>(T)=T and Δ<sup>n</sup>(T)=Δ(Δ<sup>n-1</sup>(T)), nεN. We prove that the sequence {Δ<sup>n</sup>(T)}<sub>nεN</sub> converges for every r×r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003. We also analyze the regularity of the limit function.
publishDate 2011
dc.date.none.fl_str_mv 2011-01-30
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/84303
url http://sedici.unlp.edu.ar/handle/10915/84303
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0001-8708
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2010.08.012
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
1591-1620
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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