Convergence of Aluthge iteration in semisimple Lie groups
type: Item
instance of: scholarly article
title: Convergence of Aluthge iteration in semisimple Lie groups
zbMATH Open document ID: 1305.22012
author: Tin-Yau Tam
author: Mary Clair Thompson
published in: Journal of the Mathematical Society of Japan
publication date: 2015-01-06T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.jmsj/1414090237
review text: Let \(0 < \lambda <1\). The \(\lambda\)-Aluthge transform of a complex matrix \(X\) with the polar decomposition \(X=UP\) is defined to be \(\Delta_\lambda(X):=P^\lambda UP^{1-\lambda}\) and the \(\lambda\)-Aluthge sequence \(\{\Delta_\lambda^m(X)\}_{n=1}^\infty\) is defined by \(\Delta_\lambda^m:=\Delta_\lambda(\Delta_\lambda^{m-1}(X))\) with \(\Delta_\lambda^1(X):=\Delta_\lambda(X)\). It is known that under certain conditions this sequence is convergent. \textit{J. Antezana} et al. [Adv. Math. 226, No. 2, 1591--1620 (2011; Zbl 1213.37047)] proved that the sequence converges to a normal matrix \(\Delta_\lambda^\infty(X)\) and the function \(\Delta_\lambda^\infty:\mathrm{GL}_n(\mathbb{C})\to\mathrm{GL}_n(\mathbb{C})\) defined by \(X\mapsto \Delta_\lambda^\infty(X)\) is continuous. In the paper under review, the authors extend this result in the context of real noncompact connected semisimple Lie groups.
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 47B20
zbMATH DE Number: 6383638
zbMATH Keywords: Aluthge transform
zbMATH Keywords: Aluthge iteration
zbMATH Keywords: semisimple Lie group
zbMATH Keywords: Cartan decomposition
MaRDI profile type: Publication
OpenAlex ID: W1998157997
Wikidata QID: Q115225080
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DOI: 10.2969/JMSJ/06641127
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description: scientific article; zbMATH DE number 6383638