On integral representation of radial operators

Abstract

In this article, we characterize the radial operators on weighted Bergman spaces of Reinhardt domains in $\mathbb{C}^n$, the Dirichlet and the Hardy spaces of the open unit disk $\mathbb{D}$, in terms of integral representations. We also investigate normality, compactness, spectrum and numerical ranges of these operators. Further, utilizing the theory of radial operators, we produce examples of von Neumann algebras of analytic functions on any Reinhardt domain.