Weighted multivariable operator means of positive definite operators
type: Item
instance of: scholarly article
title: Weighted multivariable operator means of positive definite operators
zbMATH Open document ID: 1314.47026
author: Miklós Pálfia
author: Dénes Petz
published in: Linear Algebra and its Applications
publication date: 2014-10-06T00:00:00Z
review text: Here, an operator means a bounded linear operator on a complex Hilbert space. The authors give a way to construct weighted operator means of two positive definite operators from arbitrary operator means due to the classical Kubo-Ando theory [\textit{F. Kubo} and \textit{T. Ando}, Math. Ann. 246, 205--224 (1980; Zbl 0412.47013)]. Then the authors give a new definition of operator means of \(n\)-tuples of positive definite operators by using the weighted operator means of two positive definite operators. To give a definition of the operator means, the authors use the so-called Bini-Meini-Poloni symmetrization process [\textit{D. A. Bini} et al., Math. Comput. 79, No. 269, 437--452 (2010; Zbl 1194.65065)] which has originally been used for making geometric means of \(n\)-tuples of positive definite matrices.
reviewed by: Takeaki Yamazaki
Mathematics Subject Classification ID: 47A64
Mathematics Subject Classification ID: 47A63
Mathematics Subject Classification ID: 47A56
zbMATH DE Number: 6351451
zbMATH Keywords: operator means
zbMATH Keywords: Kubo-Ando means
zbMATH Keywords: operator monotone functions
MaRDI profile type: Publication
full work available at URL: j.laa.2014.08.025
OpenAlex ID: W1996315691
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DOI: 10.1016/J.LAA.2014.08.025
description: scientific article; zbMATH DE number 6351451