Distributional and mean Li-Yorke chaos for weighted shifts on Fr\'echet sequence spaces

TL;DR

This paper characterizes distributional and mean Li-Yorke chaos for weighted backward shifts on general Fréchet sequence spaces and applies these results to K"othe sequence spaces.

Contribution

It provides new criteria for chaos types in weighted shifts on Fréchet and K"othe sequence spaces, expanding understanding of chaotic dynamics in these settings.

Findings

Criteria for distributional chaos in weighted shifts

Criteria for mean Li-Yorke chaos in weighted shifts

Application of chaos criteria to K"othe sequence spaces

Abstract

In this paper, we give characterizations of distributional chaos and mean Li$-$Yorke chaos for weighted backward shifts acting on general Fr\'echet sequence spaces. As an application, we derive criteria for these two types of chaos in the setting of K\"othe sequence spaces $\lambda_p(A,J)$ for $p \in \{0\}\cup [1, \infty)$ and $J=\mathbb{N}$ or $J=\mathbb{Z}$.