On Li-Yorke and distributionally chaotic direct sum operators

摘要

In this paper, sufficient conditions for the direct sum of countable linear operators on Banach spaces to be Li-Yorke chaotic (distributionally chaotic) are presented. These conditions enable us to construct a densely distributionally chaotic direct sum operator such that none of its factor operators exhibits Li-Yorke chaos. As an application, it is shown that for any b a 0, there exists an invertible operator T acting on a Hilbert space such that [a, b] = {lambda 0 : lambda T is distributionally chaotic} and for any distinct lambda(1), lambda(2) is an element of [a, b], the operators lambda T-1 and lambda T-2 have no common irregular vectors. (C) 2018 Elsevier B.V. All rights reserved.