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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Detalles Bibliográficos
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
Descripción
Sumario: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.

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