Some Spectra of Superposition Operators Generated by an Exponential Function

Sanela Halilović


In the present paper we consider the nonlinear superposition operator \(F\) in Banach spaces of sequences \(l_p\) \((1\le p\le \infty)\), generated by the function \(f(s, u) = d(s) + a^{ku} - 1\), with \(a > 1\) and \(k\in \mathbb{R}\setminus\{0\}\). We find out the Rhodius spectra \(\sigma_R(F)\) and the Neuberger spectra \(\sigma_N(F)\) of these operators, depending on the values of \(k\).


Superposition operator; Rhodius spectrum; Neuberger spectrum; Frechet derivative

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