Maximal distributional chaos of weighted shift operators on Kothe sequence spaces

During the last ten some years, many research works were devoted to the chaotic behavior of the weighted shift operator on the Kothe sequence space. In this note, a sufficient condition ensuring that the weighted shift operator B (w) (n) : lambda (p) (A) -> lambda (p) (A) defined on the Kothe sequence space lambda (p) (A) exhibits distributional E >-chaos for any 0 < E > < diam lambda (p) (A) and any n a a"center dot 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 E >-chaos for any 0 < E > < diam lambda (p) (A).