Mean Li-Yorke chaos for a sequence of operators on Banach spaces
Jian Li, Xinsheng Wang, Jianjie Zhao
TL;DR
This work extends mean equicontinuity and mean sensitivity from single operators to sequences of bounded linear operators on Banach spaces, establishing a dichotomy and a robust set of equivalent criteria. It develops a comprehensive mean Li-Yorke chaos framework for sequences, proving equivalences between mean LY chaos, mean LY pairs, and absolutely mean irregular vectors, and obtaining dense-chaos refinements via Mycielski’s theorem. The paper further analyzes submultiplicative and almost-commuting sequences, deriving invariant-subspace and dense-irregular-vector results that tie chaos to structural properties. Collectively, these results generalize classical single-operator chaos theory to non-autonomous operator families and have implications for discretizations of dynamics such as $C_0$-semigroups.
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.