Hypercyclic and mixing operator semigroups

We describe a class of topological vector spaces admitting a mixing uniformly continuous operator group $\{T_t\}_{t\in\C^n}$ with holomorphic dependence on the parameter $t$. This result covers those existing in the literature. We also<br/>describe a class of topological vector spaces admitting no supercyclic strongly continuous operator semigroups $\{T_t\}_{t\geq 0}$.