MAXIMAL DISTRIBUTIONAL CHAOS OF WEIGHTED SHIFT OPERATORS ON K?THE SEQUENCE SPACES

摘要

During the last ten some years, many research works were devoted to the chaotic behavior of the weighted shift operator on the K?the sequence space. In this note, a sufficient condition ensuring that the weighted shift operator B_w~n: λ_p(A) → λ_p(A) defined on the K?the sequence space λ_p(A) exhibits distributional ε-chaos for any 0 < ε < diam λ_p(A) and any n ∈ N is obtained. Under this assumption, the principal measure of B_w~n is equal to 1. In particular, every Devaney chaotic shift operator exhibits distributional ε-chaos for any 0 < ε < diam λ_p(A).