How does look the spectrum of an endomorphtsm of the disc-algebra?

A theorem on the spectrum of an operator on a pair of Banach spaces is presented. It implies the Kamowitz–Scheinberg theorem on the spectrum of automorphisms of a semi-simple commutative Banach algebra. Some general properties of endomorphisms of uniform algebras are described. There is given a compactness criterion of the sum of weighted endomorphisms, the cases of stability of the spectrum under pertubations of the substitution function are considered. Also new examples of spectra of automorphisms are given, the spectra of weighted endomorphisms corresponding to the conformal automorphisms of the disc are completely described.