DYNAMICS OF THE DILATION WEIGHTED COMPOSITION OPERATORS

B Yousefi,F Ershad

doi:10.12732/ijpam.v100i3.8

Abstract

In this paper we investigate the hypercyclicity of adjoint of a special weighted composition operators on Hilbert spaces of analytic functions on the open unit disc. AMS Subject Classification: 47B37, 47B38

Highlights

A bounded linear operator T on a Hilbert space H is said to be hypercyclic if there exists a vector x ∈ H for which the orbit Orb(T, x) = {T nx : n ∈ N} is dense in H and in this case we refer to x as a hypercyclic vector for T
The holomorphic self maps of the open unit disk U are divided into classes of elliptic and non-elliptic
Let H be a Hilbert space of analytic functions on the open unit disk U and let ψ be a dilation of the open unit disk U

Summary

Introduction

The holomorphic self maps of the open unit disk U are divided into classes of elliptic and non-elliptic. (see [6]) Suppose ψ is a holomorphic self-map of U that is not an elliptic automorphism. The unique attracting point w in the above proposition is called the DenjoyWolff point of ψ, and ψ is called a dilation of the open unit disk.

Results

Conclusion