Toeplitz Operators on the Super-sphere of Dimension $(2\mid 2)$

In this paper we present the boundedness condition of the Toeplitz super-operators and we describe the quasi-Toeplitz operators over classical Bergman space with quasi-homogeneous  symbols. Finally, we proved that every even super-operator acting over the Bergman super-space  in the super-sphere can be written as a Toeplitz super-operator.