Convergence of the Iterated Aluthge Transform Sequence for Diagonalizable Matrices II: λ-Aluthge Transform
Let λ∈ (0,1) and let T be a r x r complex matrix with polar decomposition T=U|T|. Then, the λ- Aluthge transform is defined by Δλ(T)= |T|λU |T |1-λ. Let Δnλ(T) denote the n-times iterated Aluthge transform of T, n ∈ N. We prove that the sequence {Δnλ(T)} n ∈ N converges for every r x r diagonalizabl...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2008 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/100305 |
| Acceso en línea: | http://hdl.handle.net/11336/100305 |
| Access Level: | acceso abierto |
| Palabra clave: | ALUTHGE TRANSFORM POLAR DECOMPOSITION SIMILARITY ORBIT STABLE MANIFOLD THEOREM https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Let λ∈ (0,1) and let T be a r x r complex matrix with polar decomposition T=U|T|. Then, the λ- Aluthge transform is defined by Δλ(T)= |T|λU |T |1-λ. Let Δnλ(T) denote the n-times iterated Aluthge transform of T, n ∈ N. We prove that the sequence {Δnλ(T)} n ∈ N converges for every r x r diagonalizable matrix T. We show regularity results for the two parameter map (λ , T) → Δ ∞ λ(T), and we study for which matrices the map (0,1) ∋ λ → Δ∞ λ(T) is constant. |
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