LAUSR

Abstract 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 ] = { λ > 0 : λ T is distributionally chaotic } and for any distinct λ 1 , λ 2 ∈ [ a , b ] , the operators λ 1 T and λ 2 T have no common irregular vectors.