Weighted geometric mean of \(n\)-operators with \(n\)-parameters
type: Item
instance of: scholarly article
title: Weighted geometric mean of \(n\)-operators with \(n\)-parameters
zbMATH Open document ID: 1189.47019
author: Changdo Jung
author: Yongdo Lim
author: Takeaki Yamazaki
author: Hosoo Lee
published in: Linear Algebra and its Applications
publication date: 2010-02-09T00:00:00Z
review text: Based on the geometric mean defined by \textit{C.\,D.\thinspace Jung}, \textit{H.\,S.\thinspace Lee} and \textit{T.\,Yamazaki} [Linear Algebra Appl.\ 431, No.\,9, 1477--1488 (2009; Zbl 1172.47017)], the authors introduce a weighted geometric mean of \(n\) operators with \(n\) parameters. It needs \(n\) parameters for weights at the outset, but does not require enormous calculations to get a concrete form. The final weights can be described by a simple form if the \(n\)-tuple of operators is commutative.
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 47A64
Mathematics Subject Classification ID: 47A63
Mathematics Subject Classification ID: 47L25
zbMATH DE Number: 5667884
zbMATH Keywords: positive operators
zbMATH Keywords: Thompson metric
zbMATH Keywords: geometric mean of \(n\)-operators
zbMATH Keywords: weighted geometric mean of \(n\)-operators
MaRDI profile type: Publication
full work available at URL: j.laa.2009.11.013
OpenAlex ID: W2010978052
cites work: Geometric means
cites work: Q3425149
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cites work: Convexity of the geodesic distance on spaces of positive operators
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DOI: 10.1016/J.LAA.2009.11.013
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description: scientific article; zbMATH DE number 5667884