Systems of operator equations and perturbation of spectral subspaces of commuting operators
type: Item
instance of: scholarly article
title: Systems of operator equations and perturbation of spectral subspaces of commuting operators
zbMATH Open document ID: 0657.47021
author: Werner J. Ricker
author: Alan McIntosh
author: Alan J. Pryde
published in: Michigan Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: Let \(\{A_ j:1\leq j\leq m\}\) be a set of commuting continuous linear operators on a Banach space X and let \(\{B_ j:1\leq j\leq m\}\) be a set of commuting continuous linear operators on a Banach space Y. The authors prove the existence and uniqueness of a continuous linear operator Q:Y\(\to X\) satisfying the system of equations \(A_ jQ-QB_ j=U_ j\) (1\(\leq j\leq m)\), where \(U_ j:Y\to X\) (1\(\leq j\leq m)\) are given continuous linear operators. Estimates for the norm \(\| Q\|\) are also given. The results are applied to the perturbation of spectra and spectral subspaces of classes of commuting m-tuples of operators. The equation \[ \sum^{m}_{j=1}A_ jQB_ j=U\quad with\quad U\in L(Y,X) \] is also studied and the existence of a unique solution is proved and the norm \(\| Q\|\) is estimated.
Mathematics Subject Classification ID: 47A62
zbMATH DE Number: 4073781
zbMATH Keywords: commuting continuous linear operators on a Banach space
zbMATH Keywords: perturbation of spectra and spectral subspaces of classes of commuting m-tuples of operators
zbMATH Keywords: existence of a unique solution
reviewed by: Walter Petry
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003681
OpenAlex ID: W1994492982
DOI: 10.1307/MMJ/1029003681
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description: scientific article; zbMATH DE number 4073781