Eigenvalues of Toeplitz Operators on the Annulus and Neil Algebra

TL;DR

This paper improves understanding of eigenvalues for self-adjoint Toeplitz operators on the annulus and Neil algebra by leveraging Sarason Hardy spaces, potentially guiding a broader theory of Toeplitz operators.

Contribution

It introduces new results on eigenvalues of Toeplitz operators on the annulus and Neil algebra using Hardy space techniques, advancing the theoretical framework.

Findings

Improved eigenvalue results for Toeplitz operators on the annulus.

Application of Hardy space methods to Neil algebra Toeplitz operators.

Potential for a general theory of Toeplitz operators with respect to algebras.

Abstract

By working with all collection of all the Sarason Hilbert Hardy spaces for the annulus algebra an improvement to the results of Aryana and Clancey on eigenvalues of self adjoint Toeplitz operators on an annulus is obtained. The ideas are applied to Toeplitz operators on the Neil algebra. These examples may provide a template for a general theory of Toeplitz operators with respect to an algebra.