Distributional and mean Li-Yorke chaos for weighted shifts on Fréchet sequence spaces

In this paper, we give characterizations of distributional chaos and mean Li$-$Yorke chaos for weighted backward shifts acting on general Fréchet sequence spaces. As an application, we derive criteria for these two types of chaos in the setting of Köthe sequence spaces ${\lambda }_p(A,J)$ for $p\in \{0\}\cup [1,\mathrm{\infty })$ and $J=\mathbb{N}$ or $J=\mathbb{Z}$.