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).