Compact endomorphisms of Banach algebras of infinitely differentiable functions

Abstract

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.

Improved version, to appear in Journal of the LMS. 16 pages LaTeX