Compact endomorphisms of Banach algebras of infinitely differentiable   functions
  We consider non-zero endomorphisms of the Dales and Davie algebras of infinitely differentiable functions on intervals in the real line. We discuss necessary and sufficient conditions for a selfmap of the interval to induce a compact endomorphism of these algebras. We also determine the spectra of these compact endomorphisms. 
J.F. Feinstein, H. Kamowitz