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On some numerical ranges for nonlinear operators. (Italian) Zbl 0940.47052

Summary: We discuss some numerical ranges for Lipschitz continuous nonlinear operators and their relations to spectral sets. In particular, we show that the spectrum defined by R. I. Kachurovskij [Dokl. Akad. Nauk SSSR 188, 274-277 (1969; Zbl 0197.40402)] for Lipschitz continuous operators is contained in the so-called polynomial hull of the numerical range introduced by A. Rhodius [Acta Sci. Math. 47, 465-470 (1984; Zbl 0575.47005)].

MSC:

47J10 Nonlinear spectral theory, nonlinear eigenvalue problems
47A12 Numerical range, numerical radius
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
65F99 Numerical linear algebra
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
47J25 Iterative procedures involving nonlinear operators
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