We show that an invertible bilateral weighted shift is strongly structurally stable if and only it has the shadowing property. also exhibit a K{o}the sequence space supporting frequently hypercyclic shift, but no chaotic shifts.

Abstract A continuous linear operator on a Fréchet space $$\mathcal {X}$$ X is frequently hypercyclic if there exists vector x such that for any nonempty open subset $$U\subset \mathcal U ⊂ the set of $$n\in \mathbb {N}\cup \{0\}$$ n <m...