Toeplitz operators on generalized harmonic Bergman spaces

TL;DR

This paper investigates Toeplitz operators with continuous symbols on generalized harmonic Bergman spaces, describing their spectra and the structure of the associated operator algebra.

Contribution

It provides a description of the essential spectra and establishes a short exact sequence for the $C^{*}$-algebra generated by these Toeplitz operators.

Findings

Characterization of the essential spectra of Toeplitz operators.

Establishment of a short exact sequence for the generated $C^{*}$-algebra.

Analysis of Toeplitz operators on generalized harmonic Bergman spaces.

Abstract

We study Toeplitz operators with uniformly continuous symbols on generalized harmonic Bergman spaces of the unit ball in $\mathbb{R}^n$. We describe their essential spectra and establish a short exact sequence associated with the $C^{*}$-algebra generated by these operators.