QUASICOMPACT AND RIESZ ENDOMORPHISMS OF INFINITELY DIFFERENTIABLE LIPSCHITZ ALGEBRAS

In this note we study the endomorphisms of the infinitely differentiable Lipschitz algebras Lip(X,M,α ), which are quasicompact operators or Riesz operators. We show that under certain conditions every quasicompact or Riesz endomorphism of these algebras is necessarily power compact. Then, when Lip(X,M,α ) is a natural Banach function algebra, we determine the spectra of Riesz and quasicompact endomorphisms of this algebra.

کلیدواژه ها:

Quaicompact ، Riesz and power compact endomorphism ، infinitely differentiable Lipschitz algebra ، spectra