Iterated Aluthge transforms: a brief survey

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...

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Autores principales: Antezana, Jorge Abel, Pujals, Enrique R., Stojanoff, Demetrio
Formato: Articulo
Lenguaje:Inglés
Publicado: 2008
Materias:
Matemática
Aluthge transform
stable manifold theorem
similarity orbit
polar decomposition
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/156336
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-156336
record_format dspace
spelling I19-R120-10915-1563362023-08-16T04:06:09Z http://sedici.unlp.edu.ar/handle/10915/156336 Iterated Aluthge transforms: a brief survey Antezana, Jorge Abel Pujals, Enrique R. Stojanoff, Demetrio 2008 2023-08-15T14:51:23Z en Matemática Aluthge transform stable manifold theorem similarity orbit polar decomposition 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 Articulo Articulo http://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International (CC BY 4.0) application/pdf 29-41
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Aluthge transform
stable manifold theorem
similarity orbit
polar decomposition
spellingShingle Matemática
Aluthge transform
stable manifold theorem
similarity orbit
polar decomposition
Antezana, Jorge Abel
Pujals, Enrique R.
Stojanoff, Demetrio
Iterated Aluthge transforms: a brief survey
topic_facet Matemática
Aluthge transform
stable manifold theorem
similarity orbit
polar decomposition
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.
format Articulo
Articulo
author Antezana, Jorge Abel
Pujals, Enrique R.
Stojanoff, Demetrio
author_facet Antezana, Jorge Abel
Pujals, Enrique R.
Stojanoff, Demetrio
author_sort Antezana, Jorge Abel
title Iterated Aluthge transforms: a brief survey
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
publishDate 2008
url http://sedici.unlp.edu.ar/handle/10915/156336
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AT pujalsenriquer iteratedaluthgetransformsabriefsurvey
AT stojanoffdemetrio iteratedaluthgetransformsabriefsurvey
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