Revista de la Unión Matemática Argentina
versión On-line ISSN 1669-9637
Given an r × r complex matrix T, if is the polar decomposition of T, then the Aluthge transform is defined by Let denote the n-times iterated Aluthge transform of T, i.e. and , . 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 converges for every r × r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003.
Palabras llave : Aluthge transform; stable manifold theorem; similarity orbit; polar decomposition.