A characterization of the Schechter essential spectrum on Banach spaces and applications
type: Item
instance of: scholarly article
title: A characterization of the Schechter essential spectrum on Banach spaces and applications
zbMATH Open document ID: 1042.47002
DOI: 10.1016/S0022-247X(02)00115-4
author: Aref Jeribi
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-11-28T00:00:00Z
review text: The author characterizes the essential spectrum of a closed and densely defined linear operator \(A\) on a general Banach space \(X\) as the intersection of the spectra of \(A+K\), where \(K\) ranges either over all bounded linear operators such that \((\lambda-A)^{-1}K\in{\mathcal I}(X)\) for some \(\lambda\in\rho(A)\) or over all bounded linear operators such that \(K(\lambda-A)^{-1}\in{\mathcal I}(X)\) for some \(\lambda\in\rho(A)\). Here \(\rho(A)\) stands for the resolvent set of \(A\) and \({\mathcal I}(X)\) is an arbitrary two-sided ideal of the Banach algebra of bounded linear operators on \(X\) that is intermediate between that of the compact operators and that of the Fredholm perturbations. Some applications are given to the linear transport operator.
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 82C70
Mathematics Subject Classification ID: 47G20
Mathematics Subject Classification ID: 47N55
zbMATH DE Number: 1836758
zbMATH Keywords: Schechter essential spectrum
zbMATH Keywords: essential spectrum
zbMATH Keywords: transport operator
MaRDI profile type: Publication
cites work: Operators of Riesz type
cites work: Q3688898
cites work: Q3254057
cites work: Q5526484
cites work: Normally solvable operators and ideals associated with them
cites work: Boundary value problems in abstract kinetic theory
cites work: Spectral properties and asymptotic behavior of the linear transport equation
cites work: Sur Les Applications Lineaires Faiblement Compactes D'Espaces Du Type C(K)
cites work: On the essential spectrum
cites work: Quelques remarques sur les opérateurs de Fredholm et application à l'équation de transport
cites work: Quelques remarques sur le spectre de Weyl et applications
cites work: Une nouvelle caractérisation du spectre essentiel et application
cites work: Q4717175
cites work: Ascent, Descent, and Commuting Perturbations
cites work: Spectral methods in linear transport theory
cites work: Perturbation theory for nullity, deficiency and other quantities of linear operators
cites work: Some remarks on the essential spectrum of transport operators with abstract boundary conditions
cites work: Time asymptotic behaviour for linear transport equations with abstract boundary conditions in slab geometry
cites work: Description of the real point spectrum for a class of neutron transport operators
cites work: Q4838258
cites work: Essential spectra on spaces with the Dunford-Pettis property
cites work: Fredholm, semi-Fredholm perturbations, and essential spectra
cites work: On the essential spectrum of transport operators on L1-spaces
cites work: Sur une équation de transport intervenant en dynamique des populations
cites work: Some results on Fredholm operators, essential spectra, and application
cites work: A nonlinear boundary value problem arising in growing cell populations
cites work: Q4136031
cites work: Some properties of strictly singular operators
cites work: Spectral theory of the neutron transport operator in bounded geometries
cites work: Spectral properties of the space nonhomogeneous linearized Boltzmann operator
cites work: Q5513422
cites work: On the essential spectrum of an arbitrary operator. I
cites work: Riesz operators and Fredholm perturbations
cites work: Q5612063
cites work: Q5631480
cites work: Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator
cites work: Q5538545
cites work: Positivity in time dependent linear transport theory
cites work: The generalization and applications of Kato's perturbation theorem
cites work: On the essential spectrum of partial differential boundary problems
cites work: Q3258444
full work available at URL: s0022-247x(02)00115-4
OpenAlex ID: W2040833556
description: scientific article; zbMATH DE number 1836758