Local spectral radii and Collatz-Wielandt numbers of monic operator polynomials with nonnegative coefficients
type: Item
instance of: scholarly article
title: Local spectral radii and Collatz-Wielandt numbers of monic operator polynomials with nonnegative coefficients
zbMATH Open document ID: 0910.47007
DOI: 10.1016/S0024-3795(97)89323-8
author: Béla Nagy
author: K.-H. Förster
published in: Linear Algebra and its Applications
publication date: 1999-04-12T00:00:00Z
review text: Operator polynomials \(L(\lambda)=\lambda^{l}I-\lambda^{l-1}A_{l-1}-\cdots-\lambda A_{1}-A_{0}\) are considered, where \(A_{0},\ldots,A_{l-1}\) are nonnegative operators in an ordered Banach space \({\mathcal H}\) with normal cone \({\mathcal H}_{+}\). For \(x\in{\mathcal H}_{+}\) local characteristics mentioned in the title are defined. These quantities are characterized with the help of corresponding quantities with respect to the first companion operator and the operator function \(S(\lambda) = A_{l-1}+\lambda^{-1}A_{l-2}+\cdots+\lambda^{-l+1}A_{0}\). Some properties known in the linear case \(l=1\) are generalized to the case \(l>1\). From these local results the authors obtain results for the global spectral radius \(r(L)\), which were proved earlier under more restrictive conditions.
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 47A11
Mathematics Subject Classification ID: 47B65
zbMATH DE Number: 1100486
zbMATH Keywords: operator polynomial
zbMATH Keywords: nonnegative operator
zbMATH Keywords: spectral radius
zbMATH Keywords: Collatz-Wielandt numbers
zbMATH Keywords: local characteristics
reviewed by: Vladimir S. Pilidi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1100486