Fredholmness of Toeplitz operators on the Fock space

TL;DR

This paper investigates the Fredholm properties of Toeplitz operators on p-Fock spaces, providing a criterion based on limit operators that extends previous results from unit ball settings.

Contribution

It introduces a general Fredholm criterion for Toeplitz operators on p-Fock spaces, linking Fredholmness to the invertibility of limit operators.

Findings

Established a Fredholm criterion for Toeplitz operators on Fock spaces.

Connected Fredholm properties to invertibility of limit operators.

Extended previous results from unit ball to Fock space setting.

Abstract

The Fredholm property of Toeplitz operators on the $p$-Fock spaces $F_\alpha^p$ on $\mathbb{C}^n$ is studied. A general Fredholm criterion for arbitrary operators from the Toeplitz algebra $\mathcal{T}_{p,\alpha}$ on $F_\alpha^p$ in terms of the invertibility of limit operators is derived. This paper is based on previous work, which establishes corresponding results on the unit balls $\mathbb{B}^n$.