The iterated Aluthge transforms of a matrix converge

Autores
Antezana, Jorge Abel; Pujals, Enrique; 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.
Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Universitat Autònoma de Barcelona; España
Fil: Pujals, Enrique. Instituto Nacional de Matemática Pura y Aplicada; Brasil
Fil: Stojanoff, Demetrio. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
ALUTHGE TRANSFORM
POLAR DECOMPOSITION
PRIMARY
SECONDARY
SIMILARITY ORBIT
STABLE MANIFOLD THEOREM
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:11336/88443
Acceder
id CONICETDig_00148de29d3dcc8fc0499190e91c2b31
oai_identifier_str oai:ri.conicet.gov.ar:11336/88443
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The iterated Aluthge transforms of a matrix convergeAntezana, Jorge AbelPujals, EnriqueStojanoff, DemetrioALUTHGE TRANSFORMPOLAR DECOMPOSITIONPRIMARYSECONDARYSIMILARITY ORBITSTABLE MANIFOLD THEOREMhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given 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.Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Universitat Autònoma de Barcelona; EspañaFil: Pujals, Enrique. Instituto Nacional de Matemática Pura y Aplicada; BrasilFil: Stojanoff, Demetrio. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaAcademic Press Inc Elsevier Science2011-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/88443Antezana, Jorge Abel; Pujals, Enrique; Stojanoff, Demetrio; The iterated Aluthge transforms of a matrix converge; Academic Press Inc Elsevier Science; Advances in Mathematics; 226; 2; 1-2011; 1591-16200001-8708CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0001870810003166info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2010.08.012info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/pdf/0711.3727.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 Técnicas2025-12-23T13:44:48Zoai:ri.conicet.gov.ar:11336/88443instacron: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 13:44:48.641CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
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
ALUTHGE TRANSFORM
POLAR DECOMPOSITION
PRIMARY
SECONDARY
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
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
POLAR DECOMPOSITION
PRIMARY
SECONDARY
SIMILARITY ORBIT
STABLE MANIFOLD THEOREM
topic ALUTHGE TRANSFORM
POLAR DECOMPOSITION
PRIMARY
SECONDARY
SIMILARITY ORBIT
STABLE MANIFOLD THEOREM
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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|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.
Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Universitat Autònoma de Barcelona; España
Fil: Pujals, Enrique. Instituto Nacional de Matemática Pura y Aplicada; Brasil
Fil: Stojanoff, Demetrio. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
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|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.
publishDate 2011
dc.date.none.fl_str_mv 2011-01
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/11336/88443
Antezana, Jorge Abel; Pujals, Enrique; Stojanoff, Demetrio; The iterated Aluthge transforms of a matrix converge; Academic Press Inc Elsevier Science; Advances in Mathematics; 226; 2; 1-2011; 1591-1620
0001-8708
CONICET Digital
CONICET
url http://hdl.handle.net/11336/88443
identifier_str_mv Antezana, Jorge Abel; Pujals, Enrique; Stojanoff, Demetrio; The iterated Aluthge transforms of a matrix converge; Academic Press Inc Elsevier Science; Advances in Mathematics; 226; 2; 1-2011; 1591-1620
0001-8708
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0001870810003166
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2010.08.012
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/pdf/0711.3727.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
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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
_version_ 1852335361371406336
score 12.952241

Publicaciones similares