Iterated Aluthge transforms: a brief survey

Autores: Antezana, Jorge Abel; Pujals, Enrique R.; Stojanoff, Demetrio
Año de publicación: 2008
Idioma: inglés
Tipo de recurso: artículo
Estado: versión publicada
Descripción: Given an r × r complex matrix T, if T = U|T| is the polar de- composition of T, then the Aluthge transform is defined by ∆(T) = |T|1/2U|T|1/2. Let ∆n(T) denote the n-times iterated Aluthge transform of T, i.e. ∆0(T) = T and ∆n(T) = ∆(∆n−1(T)), n 2 N. In this paper we make a brief survey on the known properties and applications of the Aluthge trasnsorm, particularly the recent proof of the fact that the sequence {∆n(T)}n ∊ N converges for every r ×r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003.
Facultad de Ciencias Exactas
Materia: Matemática
Aluthge transform
stable manifold theorem
similarity orbit
polar decomposition
Nivel de accesibilidad: acceso abierto
Condiciones de uso: http://creativecommons.org/licenses/by/4.0/
Repositorio
Institución: Universidad Nacional de La Plata
OAI Identificador: oai:sedici.unlp.edu.ar:10915/156336

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spelling	Iterated Aluthge transforms: a brief surveyAntezana, Jorge AbelPujals, Enrique R.Stojanoff, DemetrioMatemáticaAluthge transformstable manifold theoremsimilarity orbitpolar decompositionGiven an r × r complex matrix T, if T = U\|T\| is the polar de- composition of T, then the Aluthge transform is defined by ∆(T) = \|T\|1/2U\|T\|1/2. Let ∆n(T) denote the n-times iterated Aluthge transform of T, i.e. ∆0(T) = T and ∆n(T) = ∆(∆n−1(T)), n 2 N. In this paper we make a brief survey on the known properties and applications of the Aluthge trasnsorm, particularly the recent proof of the fact that the sequence {∆n(T)}n ∊ N converges for every r ×r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003.Facultad de Ciencias Exactas2008info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf29-41http://sedici.unlp.edu.ar/handle/10915/156336enginfo:eu-repo/semantics/altIdentifier/issn/1669-9637info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-12-23T11:42:41Zoai:sedici.unlp.edu.ar:10915/156336Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-12-23 11:42:41.904SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv	Iterated Aluthge transforms: a brief survey
title	Iterated Aluthge transforms: a brief survey
spellingShingle	Iterated Aluthge transforms: a brief survey Antezana, Jorge Abel Matemática Aluthge transform stable manifold theorem similarity orbit polar decomposition
title_short	Iterated Aluthge transforms: a brief survey
title_full	Iterated Aluthge transforms: a brief survey
title_fullStr	Iterated Aluthge transforms: a brief survey
title_full_unstemmed	Iterated Aluthge transforms: a brief survey
title_sort	Iterated Aluthge transforms: a brief survey
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 stable manifold theorem similarity orbit polar decomposition
topic	Matemática Aluthge transform stable manifold theorem similarity orbit polar decomposition
dc.description.none.fl_txt_mv	Given an r × r complex matrix T, if T = U\|T\| is the polar de- composition of T, then the Aluthge transform is defined by ∆(T) = \|T\|1/2U\|T\|1/2. Let ∆n(T) denote the n-times iterated Aluthge transform of T, i.e. ∆0(T) = T and ∆n(T) = ∆(∆n−1(T)), n 2 N. In this paper we make a brief survey on the known properties and applications of the Aluthge trasnsorm, particularly the recent proof of the fact that the sequence {∆n(T)}n ∊ N converges for every r ×r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003. Facultad de Ciencias Exactas
description	Given an r × r complex matrix T, if T = U\|T\| is the polar de- composition of T, then the Aluthge transform is defined by ∆(T) = \|T\|1/2U\|T\|1/2. Let ∆n(T) denote the n-times iterated Aluthge transform of T, i.e. ∆0(T) = T and ∆n(T) = ∆(∆n−1(T)), n 2 N. In this paper we make a brief survey on the known properties and applications of the Aluthge trasnsorm, particularly the recent proof of the fact that the sequence {∆n(T)}n ∊ N converges for every r ×r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003.
publishDate	2008
dc.date.none.fl_str_mv	2008
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/10915/156336
url	http://sedici.unlp.edu.ar/handle/10915/156336
dc.language.none.fl_str_mv	eng
language	eng
dc.relation.none.fl_str_mv	info:eu-repo/semantics/altIdentifier/issn/1669-9637
dc.rights.none.fl_str_mv	info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International (CC BY 4.0)
eu_rights_str_mv	openAccess
rights_invalid_str_mv	http://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International (CC BY 4.0)
dc.format.none.fl_str_mv	application/pdf 29-41
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repository.name.fl_str_mv	SEDICI (UNLP) - Universidad Nacional de La Plata
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Iterated Aluthge transforms: a brief survey

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