C-selfadjoint product of a composition operator and a maximal differential operator on the Fock space

In this paper, we are interested in operators arising from the product of a weighted composition operator and a maximal differential operator on the Fock space. Let T-max and C-u,C-phi denote a maximal differential operator and a weighted composition operator, respectively. We characterize some C-selfadjoint operators Cu,phi Tmax with respect to special conjugations C. Moreover, we obtain a partial characterization of hermitian operator C phi Tmax.