C-selfadjointness of the product of a composition operator and a maximal differentiation operator

Abstract

Let ϕ be an automorphism of D . In this paper, we consider the operator C ϕ D ψ 0 ,ψ 1 on the Hardy space H 2 which is the products of composition and the maximal differential operator. We characterize these operators which are C -selfadjoint with respect to some conjugations C . Moreover, we find all hermitian operators C ϕ D ψ 0 ,ψ 1 , when ϕ is a rotation.