Essential spectral radius of quasicompact endomorphisms of Lipschitz algebras

Abstract

We establish a formula for the essential spectral radius of an endomorphism $T$ of Lipschitz algebras under a condition which is equivalent to the quasicompactness of the endomorphism $T$. We also conclude a necessary and sufficient condition for an endomorphism of these algebras to be Riesz. Finally, we get a relation for the spectrum and the set of eigenvalues of a quasicompact and Riesz endomorphism of these algebras.