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.


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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