Fredholmness of Toeplitz operators on the Fock space

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 ${\mathbb{B}}^n$.