Weighted composition operators on the Fock space

In this paper, we discuss the compactness, invertibility and isometry of the operators on the Fock space formed by multiplying a weighted composition operator with the adjoint of another weighted composition operator to form either $W_{g,\psi }{W}_{f,\phi }^{\ast }$ or $W_{g,\psi }^{\ast }{W}_{f,\phi }$.