Dense uniform Li-Yorke chaos for linear operators on a Banach space

TL;DR

This paper investigates conditions under which linear operators on Banach spaces exhibit dense uniform Li-Yorke chaos, establishing equivalences and demonstrating the abundance of such chaotic operators, especially for weighted shift operators.

Contribution

It provides new sufficient and equivalent conditions for dense uniform Li-Yorke chaos in linear operators on Banach spaces, including specific results for weighted shift operators.

Findings

Dense uniform Li-Yorke chaos can be characterized by certain conditions.

Li-Yorke chaos is equivalent to dense uniform Li-Yorke chaos for weighted shifts.

There are many densely uniformly Li-Yorke chaotic operators.

Abstract

This paper focuses on the dense uniform Li-Yorke chaos for linear operators on a Banach space. Some sufficient conditions and equivalent conditions are established under which the dynamical system is densely uniformly Li-Yorke chaotic. It is shown that there are plenty of densely uniformly Li-Yorke chaotic operators. For unilateral backward weighted shifts and bilateral backward weighted shifts on $\ell^p$, it is shown that Li-Yorke chaos is equivalent to dense uniform Li-Yorke chaos.