Mean Li-Yorke chaos for a sequence of operators on Banach spaces

TL;DR

This paper investigates mean Li-Yorke chaos in sequences of bounded linear operators on Banach spaces, establishing criteria and dichotomies for mean equicontinuity, mean sensitivity, and chaos.

Contribution

It introduces new criteria and results for mean Li-Yorke chaos in sequences of operators, extending the understanding of chaotic behavior in Banach space dynamics.

Findings

Dichotomy for mean equicontinuity and mean sensitivity established.

Criteria for mean Li-Yorke chaos developed.

Analysis of chaos for submultiplicative sequences included.

Abstract

In this paper, we obtain the dichotomy for mean equicontinuity and mean sensitivity for a sequence of bounded linear operators from a Banach space to a normed linear space. The mean Li-Yorke chaos for sequences and submultiplicative sequences of bounded linear operators are also studied. Furthermore, several criteria for mean Li-Yorke chaos are established.