Composition operator induced by φ(z) = sz + t for which |s|≤1, |t|<1 and |s|+|t|≤1

Abstract

We study in this paper the composition operator that is induced by φ(z) = sz + t. We give a characterization of the adjoint of composiotion operators generated by self-maps of the unit ball of form φ(z) = sz + t for which |s|≤1, |t|<1 and |s|+|t|≤1. In fact we prove that the adjoint is a product of toeplitz operators and composition operator. Also, we have studied the compactness of Cφ and give some other partial results.