We prove that for any n ≥ 1 there exist n × n matrices A and B such that for any vector x ∈ R with a nonzero first component, the orbit of x under the action of the semigroup generated by A and B is dense in R. As a corollary, we prove that for a large set of diagonal matrices A and B and any vector V with nonzero entries, the orbit of any vector under the semigroup generated by the affine maps...

We characterize disjoint hypercyclic and supercyclic tuples of unilateral Rolewicz-type operators on $c_0(\N)$ $\ell^p(\N)$, $p \in [1, \infty)$, which are a generalization the backward shift operator. show that hypercyclicity supercyclicity equivalent among subfamily these always satisfy Disjoint Hypercyclicity Criterion. also simultaneous \infty)$.

For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and‎ ‎a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$‎, ‎it is shown that the strong Banach-Saks-ness of all evaluation‎ ‎operators on ${mathcal M}$ is a sufficient condition for the weak‎ ‎Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in‎ ‎Y^*$‎, ‎the evaluation op...

for suitable banach spaces $x$ and $y$ with schauder decompositions and‎ ‎a suitable closed subspace $mathcal{m}$ of some compact operator space from $x$ to $y$‎, ‎it is shown that the strong banach-saks-ness of all evaluation‎ ‎operators on ${mathcal m}$ is a sufficient condition for the weak‎ ‎banach-saks property of ${mathcal m}$, where for each $xin x$ and $y^*in‎ ‎y^*$‎, ‎the evaluation op...