Generalized \(M\)-matrices and ordered Banach algebras
type: Item
instance of: scholarly article
title: Generalized \(M\)-matrices and ordered Banach algebras
zbMATH Open document ID: 1019.15011
DOI: 10.1016/S0024-3795(02)00552-9
author: Gerd Herzog
published in: Linear Algebra and its Applications
publication date: 2003-05-04T00:00:00Z
review text: A matrix \(A\in \mathbb{R}^{n\times n}\) is an \(M\)-matrix if and only if the mapping \(x\mapsto-Ax\) is quasimonotone increasing (qmi) and if the right spectral bound of \(-A\) is negative. Here qmi is meant with respect to the natural cone \(K=\{x\in \mathbb{R}^n: x_k\geq 0\}\). One possibility of generalizing \(M\)-matrices is to consider qmi linear mappings on \(\mathbb{R}^n\) with respect to other cones \(K\subseteq \mathbb{R}^n\). The paper presents results on such mappings in the Banach algebra setting and discusses some special cones. Moreover, by means of one-sided estimates it is possible to get informations on the right spectral bound of qmi mappings.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 47B60
zbMATH DE Number: 1903563
zbMATH Keywords: quasimonotonicity
zbMATH Keywords: exponential positivity
zbMATH Keywords: Banach algebras
zbMATH Keywords: cone
zbMATH Keywords: spectral bound
reviewed by: Rodica Covaci
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1903563