Stability of factorization of polynomial operator pencils
type: Item
instance of: scholarly article
title: Stability of factorization of polynomial operator pencils
zbMATH Open document ID: 0547.47008
DOI: 10.1007/BF01083142
author: N. E. Zubov
publication date: 1983-01-01T00:00:00Z
review text: The authors assume the existence of a factorization \(P(\lambda)=P_ 1(\lambda)\cdot P_ 2(\lambda)\) for an operator pencil \(C\ni\lambda \to P(\lambda)=\lambda^ n1_ E+\lambda^{n-1}A_ 1+...+A_ n\) where \(A_ 1,...,A_ n\) are bounded operators in a Banach space E. They discuss some properties of factorizations of operator pencils from some neighbourhood of \(P(\lambda)\). Let us assume that \(P(\lambda\),\(\mu)\) depends analytically on a (local) parameter \(\mu \in C\), \(P(\lambda,0)=P(\lambda).\) Some condition for the existence of a factorization \(P(\lambda,\mu)=P_ 1(\lambda,\quad\mu )\cdot P_ 2(\lambda,\mu)\) with \(P_ i(\lambda,0)=P_ i(\lambda), P_ i(\lambda,\mu)\) depends analytically on \(\mu \in C (i=1,2)\), is given.
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 47A68
Mathematics Subject Classification ID: 47A60
zbMATH DE Number: 3872097
zbMATH Keywords: proper factorization
zbMATH Keywords: stable factorization
zbMATH Keywords: factorizations of operator pencils
MaRDI profile type: Publication
cites work: Resultants of matrix polynomials
cites work: Perturbation Theory for Divisors of Operator Polynomials
cites work: On the solutions of analytic equations
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3872097