ON THE HYPERBOLIC WEIGHTED COMPOSITION OPERATORS

B Yousefi,G Moghimi

doi:10.12732/ijpam.v108i1.2

Abstract

In this present paper, we investigate the hypercyclicity of a hyperbolic weighted composition operator acting on some Banach spaces of holomorphic functions on the open unit ball in C N.

Highlights

Suppose that X is a separable Banach space of analytic functions on the open unit ball BN
The set of all multipliers of X is denoted by M (X ) and it is well-known that M (X ) ⊆ H∞(BN )
Theorem 1.1. Suppose ψ is a holomorphic self-map of the open unit ball BN without interior fixed point

Summary

Introduction

Suppose that X is a separable Banach space of analytic functions on the open unit ball BN . For the algebra B(X ) of all bounded linear operators on a Banach space X , the weak operator topology (WOT) is the one in which a net Aα converges to A if Aαx → Ax weakly, x ∈ X . The strong operator topology (SOT) is the one in which a net Aα converges to A if Aαx → Ax, x ∈ X .

Results

Conclusion