Convergence of the iterated Aluthge transform sequence for diagonalizable matrices
Given an r × r complex matrix T, if T = U | T | is the polar decomposition of T, then, the Aluthge transform is defined byΔ (T) = | T |1 / 2 U | 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 {Δ...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2007 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/99841 |
| Acesso em linha: | http://hdl.handle.net/11336/99841 |
| Access Level: | acceso abierto |
| Palavra-chave: | ALUTHGE TRANSFORM POLAR DECOMPOSITION SIMILARITY ORBIT STABLE MANIFOLD THEOREM https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | Given an r × r complex matrix T, if T = U | T | is the polar decomposition of T, then, the Aluthge transform is defined byΔ (T) = | T |1 / 2 U | 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∞ (ṡ) 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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