Adjoints of Generalized Composition Operators with Linear Fractional Symbol

Abstract

Given a positive integer n and φ : U → U, an analytic self-map of the open unit disc in the complex plane, the generalized composition operator Cφ(n) is defined by Cφ(n)f = f (n) ◦ φ for f belonging to some Hilbert space of analytic functions on U. In this paper, we investigate some properties of generalized composition operators on the weighted Hardy spaces. Then we obtain adjoints of generalized composition operators with linear fractional symbol acting on the Hardy, Bergman and Dirichlet spaces.

Keywords

• Generalized composition operator
• Adjoint
• Weighted Hardy space