Weighted backward shift operators with invariant distributionally scrambled subsets

Abstract

We obtain a sufficient condition to ensure that weighted backward shift operators on Köthe sequence spaces ${\lambda }_p\left(A\right)$ admit an invariant distributionally $\epsilon$-scrambled subset for any $0<\epsilon <diam{\lambda }_p\left(A\right)$. In particular, every Devaney chaotic weighted backward shift operator on ${\lambda }_p\left(A\right)$ supports such a subset.