Dense Uniform Li-Yorke Chaos for Linear Operators on a Banach Space

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 ℓp, it is shown that Li-Yorke chaos is equivalent to dense uniform Li-Yorke chaos.