Quasicompact and Riesz composition operators on Banach spaces of Lipschitz functions on pointed metric spaces

Abstract

In this paper, we study quasicompact and Riesz composition operators on Banach spaces of Lipschitz–Holder functions on pointed metric spaces. For a composition operator T on these spaces, we give an upper bound for $$r_e(T)$$ , the essential spectral radius of T, and establish a formula for $$r_e(T)$$ whenever metric spaces are compact. We also give some necessary and some sufficient conditions that a composition operator T on these spaces to be quasicompact or Riesz. Finally, we get a relation for the set of eigenvalues and the spectrum of a quasicompact and Riesz composition operator on these spaces.