Weighted Composition Operators On Spaces Of Analytic Functions

The study of composition operators links analytic function theory and operator theory. Its main goal is to use some results and methods of classical analytic function theory to exploit some of the most basic questions, about linear operators and function spaces; at the same time, using operator theory as a tool to study the classical questions in function theory. The study of composition operator may be dated to the pioneering work of E.Nordgen[1] on the mid 1960's. Weighted composition operators are the genelization of composition operators and analytic Toeplitz operators. Back in 1964 Forelli[2] showed that every isometry on H~p for 1 < p <∞ and p ≠ 2 is a assentially weighted composition operator , weighted composition operator also appeared in recent works of [3],[4] and [5].This thesis consists of four chapters as follows: Chapter 1 contains of some well known results about weighted Hardy space and weighted composition operator. In chapter 2 we discuss the convergence of sequence of operators on weighted Hardy spaces. Chapter 3 devotes to study the spectrum of weighted composition operator. In chapter 4 we characterize the compactness of the difference of two weighted composition operators.