IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Iterated Aluthge transforms: a brief survey
Autor/es:
J. ANTEZANA, E. PUJALS Y D. STOJANOFF
Revista:
REVISTA DE LA UNIóN MATEMáTICA ARGENTINA
Editorial:
UMA
Referencias:
Lugar: Buenos Aires; Año: 2008 vol. 49 p. 29 - 29
ISSN:
0041-6932
Resumen:
Given an r × r complex matrix T, if T = U|T| is the polar decomposition of T, then, the Aluthge transform is defined by D(T) = |T|1/2U|T|1/2. Let Dn(T) denote the n-times iterated Aluthge transform of T, i.e. D0(T) = T and Dn(T) = D(Dn−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)}n2N converges for every r×r matrix T. This result was conjecturated by Jung, Ko and Pearcy in 2003.