On integral representation of radial operators

TL;DR

This paper characterizes radial operators on various function spaces in complex analysis using integral representations and explores their properties, also constructing examples of von Neumann algebras of analytic functions.

Contribution

It provides a comprehensive characterization of radial operators on multiple spaces and investigates their properties, introducing new examples of von Neumann algebras.

Findings

Characterization of radial operators via integral representations

Analysis of normality, compactness, spectrum, and numerical ranges

Construction of von Neumann algebras of analytic functions

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.