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THE NEUBERGER SPECTRA OF NONLINEAR SUPERPOSITION OPERATORS IN THE SPACES OF SEQUENCES

In this paper we consider the nonlinear superposition operator F in lp spaces of sequences, generated by the function f (s, u) = a (s) + u or f (s, u) = a (s) · u First we show that these operators are Fréchet differentiable. Then we find out the Neuberger spectra σN (F ) of these operators. We compare it with some other nonlinear spectra and indicate some possible applications.

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