Finite-dimensional perturbations of discrete operators and formulas for traces
type: Item
instance of: scholarly article
title: Finite-dimensional perturbations of discrete operators and formulas for traces
zbMATH Open document ID: 0656.47007
DOI: 10.1007/BF01078473
author: V. A. Lyubishkin
author: V. A. Sadovnichy
publication date: 1986-01-01T00:00:00Z
review text: Finite-dimensional perturbations \[ Lu=L_ ou+\sum^{r}_{k=1}(L_ 0u,f_ k)g_ k \] of a discrete self-adjoint operator \(L_ o\) in a Hilbert space H are considered. Let \(N(\lambda)=\sum_{\lambda_ n\leq \lambda}1=c\lambda +0(\lambda^ p)\), and \(f_ k\in D(L_ 0^{2q_ k})\), \(g_ k\in D(L_ 0^{2-q_ k})\) \((0\leq q_ k\leq 2)\). Then the operator L is discrete as well and there exists a sequence \(k_ n\to 0\) such that \(\lim_{n\to \infty}\sum^{k_ n}_{k=1}(\mu_ k-\lambda_ k)=\sum^{r}_{j=1}(L_ 0^{1-q_ j}g_ j,L_ 0^{q_ j}f_ j)\) \((\lambda_ k,\mu_ k\) are the eigenvalues of \(L_ 0\) and L, respectively). The complete proof of this theorem is written out, and three examples are given.
Mathematics Subject Classification ID: 47A55
zbMATH DE Number: 4071703
zbMATH Keywords: finite-dimensional perturbations of a discrete self-adjoint operator
reviewed by: Pavel Doktor
MaRDI profile type: Publication
cites work: Q5558613
cites work: Q5823806
cites work: Q3852704
cites work: Q5519306
cites work: Q5660209
cites work: Q5631640
cites work: Norms and Domains of the Complex Powers A B z
full work available at URL: https://doi.org/10.1007/bf01078473
OpenAlex ID: W2077025709
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4071703