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On the numerical range of some nonlinear operators in \(l_p\) spaces. (English) Zbl 1476.47040

The author discusses the spectra, numerical ranges and numerical radii for nonlinear operators introduced by I. J. Maddox and A. W. Wickstead [Proc. R. Ir. Acad., Sect. A 89, No. 1, 101–114 (1989; Zbl 0661.47048)], A. Rhodius [Math. Nachr. 72, 169–180 (1976; Zbl 0297.47059)] and E. H. Zarantonello [Bull. Am. Math. Soc. 70, 781–787 (1964; Zbl 0137.32501)], with a particular emphasis on applications to superposition operators in \(\ell_p\) sequence spaces. Several results presented with proofs are well known. Moreover, the paper contains an unusual amount of oversights and typos, and is written in a very sloppy and careless style, which makes the reading rather unpleasant.

MSC:

47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
47J10 Nonlinear spectral theory, nonlinear eigenvalue problems
47A12 Numerical range, numerical radius
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