Weighted composition operators on algebras of differentiable functions

Abstract

Let $X$ be a perfect compact plane set, $n\in \mathbb{N}$ and $D^n(X)$ be the algebra of complex-valued functions on $X$ with continuous $n$-th derivative. In this paper we study weighted composition operators on algebras $D^n(X)$. We give a necessary and sufficient condition for these operators to be compact. As a consequence, we characterize power compact composition operators on these algebras. Then we determine the spectra of Riesz weighted composition operators on these algebras.