Convergence of the iterated Aluthge transform sequence for diagonalizable matrices

Autores
Antezana, Jorge Abel; Pujals, Enrique; Stojanoff, Demetrio
Año de publicación
2007
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 byΔ (T) = | T |1 / 2 U | 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)), n ∈ N. We prove that the sequence {Δn (T)}n ∈ N converges for every r × r diagonalizable matrix T. We show that the limit Δ∞ (ṡ) is a map of class C∞ on the similarity orbit of a diagonalizable matrix, and on the (open and dense) set of r × r matrices with r different eigenvalues.
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
Fil: Pujals, Enrique. Instituto Nacional de Matemática Pura e Aplicada; 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
POLAR DECOMPOSITION
SIMILARITY ORBIT
STABLE MANIFOLD THEOREM
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/99841
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Convergence of the iterated Aluthge transform sequence for diagonalizable matricesAntezana, Jorge AbelPujals, EnriqueStojanoff, DemetrioALUTHGE TRANSFORMPOLAR DECOMPOSITIONSIMILARITY 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 byΔ (T) = | T |1 / 2 U | 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)), n ∈ N. We prove that the sequence {Δn (T)}n ∈ N converges for every r × r diagonalizable matrix T. We show that the limit Δ∞ (ṡ) is a map of class C∞ on the similarity orbit of a diagonalizable matrix, and on the (open and dense) set of r × r matrices with r different eigenvalues.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; ArgentinaFil: Pujals, Enrique. Instituto Nacional de Matemática Pura e Aplicada; BrasilFil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaAcademic Press Inc Elsevier Science2007-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/99841Antezana, Jorge Abel; Pujals, Enrique; Stojanoff, Demetrio; Convergence of the iterated Aluthge transform sequence for diagonalizable matrices; Academic Press Inc Elsevier Science; Advances in Mathematics; 216; 1; 1-12-2007; 255-2780001-8708CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2007.05.009info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/math/0604283info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/journal/advances-in-mathematics/vol/216/issue/1info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-12-23T14:39:16Zoai:ri.conicet.gov.ar:11336/99841instacron: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 14:39:16.461CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Convergence of the iterated Aluthge transform sequence for diagonalizable matrices
title Convergence of the iterated Aluthge transform sequence for diagonalizable matrices
spellingShingle Convergence of the iterated Aluthge transform sequence for diagonalizable matrices
Antezana, Jorge Abel
ALUTHGE TRANSFORM
POLAR DECOMPOSITION
SIMILARITY ORBIT
STABLE MANIFOLD THEOREM
title_short Convergence of the iterated Aluthge transform sequence for diagonalizable matrices
title_full Convergence of the iterated Aluthge transform sequence for diagonalizable matrices
title_fullStr Convergence of the iterated Aluthge transform sequence for diagonalizable matrices
title_full_unstemmed Convergence of the iterated Aluthge transform sequence for diagonalizable matrices
title_sort Convergence of the iterated Aluthge transform sequence for diagonalizable matrices
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
SIMILARITY ORBIT
STABLE MANIFOLD THEOREM
topic ALUTHGE TRANSFORM
POLAR DECOMPOSITION
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 byΔ (T) = | T |1 / 2 U | 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)), n ∈ N. We prove that the sequence {Δn (T)}n ∈ N converges for every r × r diagonalizable matrix T. We show that the limit Δ∞ (ṡ) is a map of class C∞ on the similarity orbit of a diagonalizable matrix, and on the (open and dense) set of r × r matrices with r different eigenvalues.
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
Fil: Pujals, Enrique. Instituto Nacional de Matemática Pura e Aplicada; 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 Given an r × r complex matrix T, if T = U | T | is the polar decomposition of T, then, the Aluthge transform is defined byΔ (T) = | T |1 / 2 U | 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)), n ∈ N. We prove that the sequence {Δn (T)}n ∈ N converges for every r × r diagonalizable matrix T. We show that the limit Δ∞ (ṡ) is a map of class C∞ on the similarity orbit of a diagonalizable matrix, and on the (open and dense) set of r × r matrices with r different eigenvalues.
publishDate 2007
dc.date.none.fl_str_mv 2007-12-01
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/11336/99841
Antezana, Jorge Abel; Pujals, Enrique; Stojanoff, Demetrio; Convergence of the iterated Aluthge transform sequence for diagonalizable matrices; Academic Press Inc Elsevier Science; Advances in Mathematics; 216; 1; 1-12-2007; 255-278
0001-8708
CONICET Digital
CONICET
url http://hdl.handle.net/11336/99841
identifier_str_mv Antezana, Jorge Abel; Pujals, Enrique; Stojanoff, Demetrio; Convergence of the iterated Aluthge transform sequence for diagonalizable matrices; Academic Press Inc Elsevier Science; Advances in Mathematics; 216; 1; 1-12-2007; 255-278
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/doi/10.1016/j.aim.2007.05.009
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/math/0604283
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/journal/advances-in-mathematics/vol/216/issue/1
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
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
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score 12.952241

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