Some Spectra of Superposition Operators Generated by an Exponential Function - Halilović, Sanela (Communications in Mathematics and Applications, 2021)
In the present paper we consider the nonlinear superposition operator \(F\) in Banach spaces of sequences \(l_p\) \((1\le p\le ∞)\), 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 \(σ_R(F)\) and the Neuberger spectra \(σ_N(F)\) of these operators, depending on the values of \(k\).
Keywords: Superposition operator; Rhodius spectrum; Neuberger spectrum; Frechet derivative