A note on supercyclic operators in locally convex spaces

TL;DR

This paper explores the properties of supercyclic operators in locally convex spaces, extending previous results and examining doubly power bounded operators with illustrative examples.

Contribution

It extends existing results on supercyclicity to locally convex spaces and analyzes doubly power bounded operators in this broader context.

Findings

Extended supercyclicity results to locally convex spaces

Analyzed doubly power bounded operators in this setting

Provided examples illustrating the concepts

Abstract

We treat some questions related to supercyclicity of continuous linear operators when acting in locally convex spaces. We extend results of Ansari and Bourdon and consider doubly power bounded operators in this general setting. Some examples are given.