The iterated Aluthge transforms of a 2-by-2 matrix converge.
type: Item
instance of: scholarly article
title: The iterated Aluthge transforms of a 2-by-2 matrix converge.
zbMATH Open document ID: 1045.15015
author: D. Massart
published in: Linear Algebra and its Applications
publication date: 2003-12-04T00:00:00Z
review text: The Aluthge transformation takes a complex matrix \(T=U|T|\) in polar form to the matrix \(|T|^{1/2}U|T|^{1/2}\) [cf. \textit{A. Aluthge}, Integral Equations Oper. Theory 13, No. 3, 307--315 (1990; Zbl 0718.47015)]. The author proves for \(2\times 2\) complex matrices that the iterates of the Aluthge transform always converge. \textit{T. Ando} [Aluthge transforms and the convex hull of the eigenvalues of a matrix (to appear)] proved that every limit point of the sequence of iterates of the Aluthge transform on an arbitrary matrix is normal.
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 2013061
zbMATH Keywords: Aluthge transform
zbMATH Keywords: normal matrix
zbMATH Keywords: convergence
zbMATH Keywords: polar form
zbMATH Keywords: complex matrices
zbMATH Keywords: iterates
reviewed by: Ki Hang Kim
MaRDI profile type: Publication
full work available at URL: j.laa.2003.06.002
OpenAlex ID: W2037427088
cites work: On p-hyponormal operators for \(0<p<1\)
cites work: Aluthge Transforms and the Convex Hull of the Eigenvalues of a Matrix
cites work: Q5690490
cites work: Aluthge transforms of operators
DOI: 10.1016/J.LAA.2003.06.002
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description: scientific article; zbMATH DE number 2013061