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...
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| Autores principales: | , , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2008
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/156336 |
| Aporte de: |
| Sumario: | 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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