The eigenvalues of limits of radial Toeplitz operators

TL;DR

This paper characterizes the eigenvalues of radial operators on the Bergman space that can be approximated by Toeplitz operators with bounded symbols, providing insights into their spectral properties.

Contribution

It offers a characterization of eigenvalues for a class of radial operators approximable by Toeplitz operators with bounded symbols.

Findings

Eigenvalues are characterized for radial operators approximable by Toeplitz operators.

Provides conditions under which radial operators can be approximated by Toeplitz operators.

Enhances understanding of spectral properties of radial Toeplitz operators.

Abstract

Let $A^2$ be the Bergman space on the unit disk. A bounded operator $S$ on $A^2$ is called radial if $Sz^n = \lambda_n z^n$ for all $n\ge 0$, where $\lambda_n$ is a bounded sequence of complex numbers. We characterize the eigenvalues of radial operators that can be approximated by Toeplitz operators with bounded symbols.