  In this article, first we show that the Fr\'echet 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.
