A sequence ${T_n}_{n=1}^{infty}$ of bounded linear  operators on a separable infinite dimensional Hilbert space $mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $Msubseteq mathcal{H},$ if there exists a vector $xin mathcal{H}$ such that the disk-scaled orbit ${alpha T_n x: nin mathbb{N}, alpha inmathbb{C}, | alpha | leq 1}cap M$ is dense in $M$. The goal of t...

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...