The iterated Aluthge transforms of a matrix converge
Given an r×r complex matrix T, if T=U|T| is the polar decomposition of T, then, the Aluthge transform is defined by Δ(T)=|T|<sup>1/2</sup>U|T|<sup>1/2</sup>. Let Δ<sup>n</sup>(T) denote the n-times iterated Aluthge transform of T, i.e., Δ<sup>0</sup>(T...
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| Autores principales: | , , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2011
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/84303 |
| Aporte de: |
| Sumario: | Given an r×r complex matrix T, if T=U|T| is the polar decomposition of T, then, the Aluthge transform is defined by Δ(T)=|T|<sup>1/2</sup>U|T|<sup>1/2</sup>. Let Δ<sup>n</sup>(T) denote the n-times iterated Aluthge transform of T, i.e., Δ<sup>0</sup>(T)=T and Δ<sup>n</sup>(T)=Δ(Δ<sup>n-1</sup>(T)), nεN. We prove that the sequence {Δ<sup>n</sup>(T)}<sub>nεN</sub> converges for every r×r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003. We also analyze the regularity of the limit function. |
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