MULTIPLICATION OPERATORS ON ANALYTIC FUNCTIONAL SPACES

Abstract

Let $X$ be a reflexive Banach space of functions analytic on a bounded plane domain $G$ such that for every $\lambda$ in $G$ the functional of evaluation at $\lambda$ is bounded. Assume further that $X$ contains the constants and admits multiplication by the independent variable $z$, $M_{z}$, as a bounded operator. We give sufficient conditions for $M_{z}$ to be reflexive.