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

Abstract

In this paper, we consider the nonlinear superposition operator F in lp 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 σR(F) and the Neuberger spectra σN(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.