Abstract

ANTEZANA, Jorge; PUJALS, Enrique R.  and  STOJANOFF, Demetrio. Iterated Aluthge transforms: a brief survey. Rev. Unión Mat. Argent. [online]. 2008, vol.49, n.1, pp.29-41. ISSN 0041-6932.

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.

Keywords : Aluthge transform; stable manifold theorem; similarity orbit; polar decomposition.

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