Symmetric function means of positive operators
type: Item
instance of: scholarly article
title: Symmetric function means of positive operators
zbMATH Open document ID: 0575.47001
DOI: 10.1016/0024-3795(84)90075-2
author: T. D. Morley
author: William N. jun. Anderson
author: George E. Trapp
published in: Linear Algebra and its Applications
publication date: 1984-01-01T00:00:00Z
review text: The authors study means of operators that generalize the means involving ratios of elementary symmetric functions and obtain inequalities between these means which extend many of the classical scalar inequalities. There is a relationship with electrical networks and some of the terminology is motivated by this connection. The concept of the parallel sum of two operators is important and when A and B are invertible positive operators is defined by \(A:B=(A^{-1}+B^{-1})^{-1}.\) A key inequality is known as the series parallel inequality, one special case being the arithmetic- harmonic mean inequality. Two types of means are defined and various relationships between them are obtained.
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 47A30
zbMATH DE Number: 3919124
zbMATH Keywords: means of operators
zbMATH Keywords: inequalities
zbMATH Keywords: electrical networks
zbMATH Keywords: parallel sum of two operators
MaRDI profile type: Publication
full work available at URL: 0024-3795(84)90075-2
OpenAlex ID: W2076100825
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description: scientific article; zbMATH DE number 3919124