A comparison of different spectra for nonlinear operators
type: Item
instance of: scholarly article
title: A comparison of different spectra for nonlinear operators
zbMATH Open document ID: 0956.47035
DOI: 10.1016/S0362-546X(00)85005-1
author: Jürgen Appell
author: E. De Pascale
author: A. Vignoli
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-03-07T00:00:00Z
review text: The authors express the opinion that it is only slightly exaggerated to say that the spectral theory for linear operators is one of the most important topics of functional analysis and operator theory. As a matter of fact, much information on a linear operator is ``hidden'' in it's spectrum, and thus knowing the spectrum means knowing a large part of the properties of the operator. In view of the importance of spectral theory for linear operators, it is not surprising at all that various attempts have been made to define and study spectra also for nonlinear operators. In this paper the authors discuss spectra for various classes of nonlinear operators and compare their properties from the viewpoint of the above requirements. The classes they are interested in are Fréchet differentiable operators, Lipschitz continuous operators, general continuous operators, special continuous operators, \(k\)-epi continuous, and linearly bounded operators.
reviewed by: Ulrich Kosel
Mathematics Subject Classification ID: 47J10
Mathematics Subject Classification ID: 46T20
Mathematics Subject Classification ID: 46G05
zbMATH DE Number: 1472208
zbMATH Keywords: resolvent set
zbMATH Keywords: spectrum
zbMATH Keywords: resolvent operator
zbMATH Keywords: spectral radius
zbMATH Keywords: mapping theorem
zbMATH Keywords: Gel'fand formula
zbMATH Keywords: Fréchet differentiable operators
zbMATH Keywords: Lipschitz continuous operators
zbMATH Keywords: continuous operators
zbMATH Keywords: \(k\)-epi continuous
zbMATH Keywords: linearly bounded operators
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1472208