  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
describe a class of topological vector spaces admitting no supercyclic strongly
continuous operator semigroups ${T_t}_{t\geq 0}$.
