On Essentially Normality of the Composition Operator C_σ

Abstract

  In this paper we have studied the composition operator induced by the automorphism  and discussed the adjoint of the composition of the symbol .We have look also at 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  on 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 .