Iterated Aluthge transforms: a brief survey

Autores
Antezana, Jorge Abel; Pujals, Enrique; Stojanoff, Demetrio
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Abstract. Given an r × r complex matrix T, if T = U|T| is the polar decomposition 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 ∈ 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 conjecturated by Jung, Ko and Pearcy in 2003.
Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Pujals, Enrique. Centro Nacional de Pesquisa Em Energia E Materiais; Brasil
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
Aluthge Transform
Stable manifold theorem
Similarity orbit
Polar decomposition
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/95310
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/95310
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Iterated Aluthge transforms: a brief surveyAntezana, Jorge AbelPujals, EnriqueStojanoff, DemetrioAluthge TransformStable manifold theoremSimilarity orbitPolar decompositionhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Abstract. Given an r × r complex matrix T, if T = U|T| is the polar decomposition 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 ∈ 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 conjecturated by Jung, Ko and Pearcy in 2003.Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Pujals, Enrique. Centro Nacional de Pesquisa Em Energia E Materiais; BrasilFil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaUnión Matemática Argentina2008-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/95310Antezana, Jorge Abel; Pujals, Enrique; Stojanoff, Demetrio; Iterated Aluthge transforms: a brief survey; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 49; 1; 12-2008; 29-410041-69321669-9637CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/pdf/v49n1/v49n1a04.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-12-23T13:34:24Zoai:ri.conicet.gov.ar:11336/95310instacron: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:34982025-12-23 13:34:24.532CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
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
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
Stojanoff, Demetrio
author Antezana, Jorge Abel
author_facet Antezana, Jorge Abel
Pujals, Enrique
Stojanoff, Demetrio
author_role author
author2 Pujals, Enrique
Stojanoff, Demetrio
author2_role author
author
dc.subject.none.fl_str_mv Aluthge Transform
Stable manifold theorem
Similarity orbit
Polar decomposition
topic Aluthge Transform
Stable manifold theorem
Similarity orbit
Polar decomposition
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Abstract. Given an r × r complex matrix T, if T = U|T| is the polar decomposition 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 ∈ 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 conjecturated by Jung, Ko and Pearcy in 2003.
Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Pujals, Enrique. Centro Nacional de Pesquisa Em Energia E Materiais; Brasil
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description Abstract. Given an r × r complex matrix T, if T = U|T| is the polar decomposition 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 ∈ 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 conjecturated by Jung, Ko and Pearcy in 2003.
publishDate 2008
dc.date.none.fl_str_mv 2008-12
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/11336/95310
Antezana, Jorge Abel; Pujals, Enrique; Stojanoff, Demetrio; Iterated Aluthge transforms: a brief survey; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 49; 1; 12-2008; 29-41
0041-6932
1669-9637
CONICET Digital
CONICET
url http://hdl.handle.net/11336/95310
identifier_str_mv Antezana, Jorge Abel; Pujals, Enrique; Stojanoff, Demetrio; Iterated Aluthge transforms: a brief survey; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 49; 1; 12-2008; 29-41
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/v49n1/v49n1a04.pdf
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
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 12.952241

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