Convergence of the iterated Aluthge transform sequence for diagonalizable matrices

Autores
Antezana, Jorge Abel; Pujals, Enrique R.; Stojanoff, Demetrio
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given an r × r complex matrix T ,ifT = 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 )), 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∞(·) 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.
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:10915/83247
Acceder
id SEDICI_caac2d0b27c1b603af7039aeade60432
oai_identifier_str oai:sedici.unlp.edu.ar:10915/83247
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Convergence of the iterated Aluthge transform sequence for diagonalizable matricesAntezana, Jorge AbelPujals, Enrique R.Stojanoff, DemetrioMatemáticaAluthge transformPolar decompositionSimilarity orbitStable manifold theoremGiven an r × r complex matrix T ,ifT = 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 )), 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∞(·) 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.Facultad de Ciencias Exactas2007info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf255-278http://sedici.unlp.edu.ar/handle/10915/83247enginfo:eu-repo/semantics/altIdentifier/issn/0001-8708info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2007.05.009info: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:UNLP2025-12-23T11:17:54Zoai:sedici.unlp.edu.ar:10915/83247Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-12-23 11:17:54.484SEDICI (UNLP) - Universidad Nacional de La Platafalse
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
Matemática
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 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 ,ifT = 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 )), 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∞(·) 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.
Facultad de Ciencias Exactas
description Given an r × r complex matrix T ,ifT = 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 )), 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∞(·) 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
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/10915/83247
url http://sedici.unlp.edu.ar/handle/10915/83247
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.2007.05.009
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
255-278
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
_version_ 1852334170152370176
score 12.952241

Publicaciones similares