Essential spectra, matrix operator and applications
type: Item
instance of: scholarly article
title: Essential spectra, matrix operator and applications
zbMATH Open document ID: 1209.47006
author: Salma Charfi
author: Aref Jeribi
author: Ines Walha
published in: Acta Applicandae Mathematicae
publication date: 2010-07-24T00:00:00Z
review text: In the two introductory sections of this paper, general notions of operator theory are discussed (Fredholm operators, the various notions of spectra, etc.). Then operators of the form \({A\;B\choose C\;D}\) acting in a Banach space \(X\times Y\) are considered; the operators \(A, B, C, D\) are not assumed to be bounded. A criterion is formulated under which the operator admits a closure \({\mathcal A}\). Then various types of spectra for \({\mathcal A}\) are indicated. Finally, applications are considered (delay differential equations, the Sturm-Liouville problem with the spectral parameter entering rationally, the transport equation). The exposition is not always accurate. For example, the authors write \(\lambda-T\), where \(T\) acts from the given space to another, the most important notion \(\rho_b(A_1)\) is explained too late, etc.
reviewed by: R. S. Ismagilov
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 35P05
zbMATH DE Number: 5760433
zbMATH Keywords: essential spectra
zbMATH Keywords: Fredholm operators
zbMATH Keywords: semi-Fredholm operators
zbMATH Keywords: compact operators
zbMATH Keywords: weakly compact operators
MaRDI profile type: Publication
full work available at URL: s10440-009-9547-9
OpenAlex ID: W1966404632
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DOI: 10.1007/S10440-009-9547-9
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description: scientific article; zbMATH DE number 5760433