A comparison of different spectra for nonlinear operators. (English) Zbl 0956.47035

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.


47J10 Nonlinear spectral theory, nonlinear eigenvalue problems
46T20 Continuous and differentiable maps in nonlinear functional analysis
46G05 Derivatives of functions in infinite-dimensional spaces
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