On the commutant of operators of multiplication by univalent functions

Let B be a certain Banach space consisting of continuous functions defined on the open unit disk. Let phi is an element of B be a univalent function defined on (D) over bar, and assume that M-phi denotes the operator of multiplication by phi. We characterize the structure of the operator T such that MphiT = TMphi. We show that T = M-phi for some function phi in B. We also characterize the commutant of M-phi2 under certain conditions.