Iterated Aluthge transforms: a brief survey
Abstract. Given an r × r complex matrix T, if T = U|T| is the polar decomposition of T, then, the Aluthge transform is defined by ∆ (T) = |T| 1/2U|T| 1/2 . Let ∆n(T) denote the n-times iterated Aluthge transform of T, i.e. ∆0 (T) = T and ∆n(T) = ∆(∆n−1 (T)), n ∈ N. In this paper we make a brief surv...
| 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:11336/95310 |
| Acceso en línea: | http://hdl.handle.net/11336/95310 |
| Access Level: | acceso abierto |
| Palabra clave: | Aluthge Transform Stable manifold theorem Similarity orbit Polar decomposition https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Abstract. Given an r × r complex matrix T, if T = U|T| is the polar decomposition of T, then, the Aluthge transform is defined by ∆ (T) = |T| 1/2U|T| 1/2 . Let ∆n(T) denote the n-times iterated Aluthge transform of T, i.e. ∆0 (T) = T and ∆n(T) = ∆(∆n−1 (T)), n ∈ N. In this paper we make a brief survey on the known properties and applications of the Aluthge trasnsorm, particularly the recent proof of the fact that the sequence {∆n(T)}n∈N converges for every r×r matrix T. This result was conjecturated by Jung, Ko and Pearcy in 2003. |
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