The spectra of certain nonlinear superposition operators in the spaces of sequences

Abstract

In this paper, we consider the nonlinear superposition operator F in l_p spaces of sequences (1 ≤ p ≤ ∞), generated by the function

f(s,u)=a(s) + arctan u or f(s,u) = a(s) - arctan u.

We find out the Rhodius spectra σ_R(F) and the Neuberger spectra σ_N(F) of these operators and finally the radii of these spectra. The superposition operator generated by the function f(s,u) = a(s) ∓ arccot u appears to be a special case of above mentioned operator.