Dynamics of weighted shifts on directed trees

TL;DR

This paper investigates the dynamical properties of weighted shift operators on directed trees, providing characterizations of their boundedness and conditions for hypercyclicity, weak mixing, and mixing behaviors.

Contribution

It offers new criteria for boundedness and dynamical classifications of weighted shifts on directed trees, expanding understanding of their operator dynamics.

Findings

Characterized boundedness of weighted shifts on directed trees.

Established conditions for hypercyclicity, weak mixing, and mixing.

Provided a framework for analyzing operator dynamics on complex graph structures.

Abstract

We study the dynamical behaviour of weighted shifts defined on sequence spaces of a directed tree. In particular, we characterize their boundedness as well as when they are hypercyclic, weakly mixing and mixing.