Hypercyclicity of composition operators on discrete weighted Banach spaces

TL;DR

This paper investigates when composition operators on discrete weighted Banach spaces are hypercyclic, showing they only act on small spaces and providing conditions for their boundedness and hypercyclicity.

Contribution

It characterizes bounded and hypercyclic composition operators on discrete weighted Banach spaces, focusing on their action on 'little' spaces and establishing necessary conditions for hypercyclicity.

Findings

Only composition operators on 'little' spaces are hypercyclic.

Provided criteria for boundedness of composition operators.

Established necessary conditions for hypercyclicity.

Abstract

In this paper, we study the hypercyclic composition operators on weighted Banach spaces of functions defined on discrete metric spaces. We show that the only such composition operators act on the "little" spaces. We characterize the bounded composition operators on the little spaces, as well as provide various necessary conditions for hypercyclicity.