Three results in linear dynamics

Abstract

In this article, first we show that the Fr$\acute{\textnormal{e}}$chet space $H(\Bbb D)$ cannot support strongly supercyclic weighted composition operators.

Then we compute the constant $\epsilon$ for weighted backward shifts on $\ell^p$ ($1\le p<\infty$) and $c_0$. This constant is used to find strongly hypercyclic scalar

multiples of non-invertible strongly supercyclic Banach space operators.

Finally, we give an affirmative answer to a recent open question concerning supercyclic vectors.