Invariance of distributional chaos for backward shifts

Abstract

A sufficient and necessary condition ensuring that the backward shift operator on the Köthe sequence space admits an invariant distributionally $\epsilon$-scrambled set for some $\epsilon >0$ is obtained, improving the main results in [F. Mart\'ınez-Giménez, P. Oprocha, A. Peris, J. Math. Anal. Appl., {\bf 351} (2009), 607--615].

7 pages