Perron roots of a convex combination of a cone preserving map and its adjoint
type: Item
instance of: scholarly article
title: Perron roots of a convex combination of a cone preserving map and its adjoint
zbMATH Open document ID: 0557.15008
DOI: 10.1016/0024-3795(84)90211-8
published in: Linear Algebra and its Applications
publication date: 1984-01-01T00:00:00Z
review text: The author considers generalizations of the result of Levinger and Fiedler that for a square matrix A of nonnegative real numbers, the Perron root r(t) of \((1-t)A+tA^*\) as a function of t is non-decreasing for \(t\in (0,)\) and non-increasing for \(t\in (,1).\) The setting is an operator which together with its adjoint leaves invariant a cone in an inner product space. A result similar to the Levinger-Fiedler result is obtained if the cone induces a Riesz space structure and some further natural conditions on the operator and the cone are satisfied.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 47B60
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 3887867
zbMATH Keywords: Hardy-Littlewood-Polya type inequality
zbMATH Keywords: cone preserving operator
zbMATH Keywords: Perron root
zbMATH Keywords: positive operator
zbMATH Keywords: Riesz space
author: Ivo Marek
reviewed by: Tage Bai Andersen
MaRDI profile type: Publication
full work available at URL: 0024-3795(84)90211-8
OpenAlex ID: W2060828957
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description: scientific article; zbMATH DE number 3887867