Hypercyclic and mixing operator semigroups

Abstract: 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 ${T_t}{t\geq 0}$.