Convergence of the iterated Aluthge transform sequence for diagonalizable matrices

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 conver...

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Autores principales: Antezana, Jorge Abel, Pujals, Enrique R., Stojanoff, Demetrio
Formato: Articulo
Lenguaje:Inglés
Publicado: 2007
Materias:
Matemática
Aluthge transform
Polar decomposition
Similarity orbit
Stable manifold theorem
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/83247
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-83247
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
Convergence of the iterated Aluthge transform sequence for diagonalizable matrices
topic_facet Matemática
Aluthge transform
Polar decomposition
Similarity orbit
Stable manifold theorem
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.
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 Convergence of the iterated Aluthge transform sequence for diagonalizable matrices
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
publishDate 2007
url http://sedici.unlp.edu.ar/handle/10915/83247
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AT stojanoffdemetrio convergenceoftheiteratedaluthgetransformsequencefordiagonalizablematrices
bdutipo_str Repositorios
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