Properties of the function Ф and the composition operator C Ф induced by the function Ф

Abstract EN

Let U denote the unit ball in the complex plane, the Hardy space H2 is the set of functions holomorphic on U such that with denotes then the Taylor coefficient of f .

Let be a holomorphic self-map of U, the composition operator induced by is defined on H2 by the equation In this paper we have studied the composition operator induced by the automorphism and discussed the adjoint of the composition of the symbol .We look also for some known properties on composition operators and tried to see the analogue properties in order to show how the results are changed by changing the function in U.

In order to make the work accessible to the reader, we have included some known results with the details of the proofs for some cases and proofs for the properties .