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 $$\mathbb {B}^n$$ (Hagger in Integr Equ Oper Theory 89(4):519–556, 2017).