Eigenvalues of a certain quadratic pencil of operators
type: Item
instance of: scholarly article
title: Eigenvalues of a certain quadratic pencil of operators
zbMATH Open document ID: 0677.47010
DOI: 10.1007/BF01078584
publication date: 1989-01-01T00:00:00Z
review text: In a separable Hilbert space the quadratic pencil \[ L(\lambda)=\lambda^ 2I+\lambda (\alpha A+C)+A \] is considered. Here A and C are closed linear operators, \(A\geq -\beta /2I\) \((\beta >0)\), \(\alpha\geq 0\), and the negative part of the spectrum of A is discrete. It is assumed also that \(C\geq 0\) is symmetric and is A-bounded in the sense of Kato. It is stated that the number of eigenvalues of L(\(\lambda)\) with positive real part is equal to the number of negative eigenvalues of A.
Mathematics Subject Classification ID: 47A56
zbMATH DE Number: 4109411
zbMATH Keywords: number of eigenvalues with positive real part
zbMATH Keywords: quadratic pencil
zbMATH Keywords: closed linear operators
zbMATH Keywords: negative part of the spectrum
zbMATH Keywords: number of negative eigenvalues
author: V. Pivovarchik
MaRDI profile type: Publication
cites work: Q5526485
cites work: Q5519463
cites work: Q5539991
full work available at URL: https://doi.org/10.1007/bf01078584
OpenAlex ID: W2005550689
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4109411