Iterated Aluthge transforms: a brief survey
Given an r × r complex matrix T, if T = U|T| is the polar de- composition 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 2 N. In this paper we make a brief survey on the known...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2008 |
| País: | Argentina |
| Recursos: | Universidad Nacional de La Plata |
| Repositorio: | SEDICI (UNLP) |
| Idioma: | inglés |
| OAI Identifier: | oai:sedici.unlp.edu.ar:10915/156336 |
| Acesso em linha: | http://sedici.unlp.edu.ar/handle/10915/156336 |
| Access Level: | acceso abierto |
| Palavra-chave: | Matemática Aluthge transform stable manifold theorem similarity orbit polar decomposition |
| Resumo: | Given an r × r complex matrix T, if T = U|T| is the polar de- composition 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 2 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 conjectured by Jung, Ko and Pearcy in 2003. |
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