IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
The iterated Aluthge transforms sequence of a matrix converge
Autor/es:
JORGE ANTEZANA; ENRIQUE PUJALS; DEMETRIO STOJANOFF
Revista:
ADVANCES IN MATHEMATICS
Editorial:
ACADEMIC PRESS INC ELSEVIER SCIENCE
Referencias:
Lugar: Amsterdam; Año: 2011 vol. 226 p. 1591 - 1591
ISSN:
0001-8708
Resumen:
Given an $r\times r$ complex matrix $T$, if $T=U|T|$ is the polardecomposition of $T$, then, the Aluthge transform is defined by $$\Delta\left(T \right)= |T|^{1/2} U |T |^{1/2}.$$ Let $\Delta^{n}(T)$ denote the $n$-times iterated Aluthge transform of $T$, i.e.$\Delta^{0}(T)=T$ and $\Delta^{n}(T)=\Delta(\Delta^{n-1}(T))$, $n\in\mathbb{N}$. We prove that the sequence $\{\Delta^{n}(T)\}_{n\in\mathbb{N}}$ converges for every $r\times r$  matrix $T$. This result was conjectured by Jung, Ko and Pearcy in 2003. We also analyze the regularity of the limit function.