Li-Yorke Chaos for Composition operators on Orlicz-Lorentz spaces

TL;DR

This paper characterizes when composition operators on Orlicz-Lorentz spaces exhibit Li-Yorke chaos, providing necessary and sufficient conditions and generalizing previous results to a broader functional setting.

Contribution

It introduces new criteria for Li-Yorke chaos of composition operators specifically on Orlicz-Lorentz spaces, extending prior work to a more general space class.

Findings

Derived necessary and sufficient conditions for chaos

Established equivalent conditions for Li-Yorke chaos

Generalized previous results to Orlicz-Lorentz spaces

Abstract

In this paper, we study the Li-Yorke chaotic composition operators on Orlicz-Lorentz space. In fact, necessary and sufficient conditions are given for Li-Yorke chaotic composition operator $C_{\tau}$ on $\mathbb{L}^{\varphi,h}(\mu)$. Further, we present the equivalent conditions for $C_{\tau}$ to be Li-Yorke chaotic. This paper's results are the generalization of results of [15] into Orlicz-Lorentz spaces.