The iterated Aluthge transforms of a matrix converge

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|<sup>1/2</sup>U|T|<sup>1/2</sup>. Let Δ<sup>n</sup>(T) denote the n-times iterated Aluthge transform of T, i.e., Δ<sup>0</sup>(T...

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Autores principales: Antezana, Jorge Abel, Pujals, Enrique R., Stojanoff, Demetrio
Formato: Articulo
Lenguaje:Inglés
Publicado: 2011
Materias:
Matemática
Aluthge transform
Polar decomposition
Similarity orbit
Stable manifold theorem
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/84303
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-84303
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Aluthge transform
Polar decomposition
Similarity orbit
Stable manifold theorem
spellingShingle Matemática
Aluthge transform
Polar decomposition
Similarity orbit
Stable manifold theorem
Antezana, Jorge Abel
Pujals, Enrique R.
Stojanoff, Demetrio
The iterated Aluthge transforms of a matrix converge
topic_facet Matemática
Aluthge transform
Polar decomposition
Similarity orbit
Stable manifold theorem
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|<sup>1/2</sup>U|T|<sup>1/2</sup>. Let Δ<sup>n</sup>(T) denote the n-times iterated Aluthge transform of T, i.e., Δ<sup>0</sup>(T)=T and Δ<sup>n</sup>(T)=Δ(Δ<sup>n-1</sup>(T)), nεN. We prove that the sequence {Δ<sup>n</sup>(T)}<sub>nεN</sub> 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.
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 The iterated Aluthge transforms of a matrix converge
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 iterated aluthge transforms of a matrix converge
publishDate 2011
url http://sedici.unlp.edu.ar/handle/10915/84303
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