On the Existence of Transitive and Topologically Mixing Semigroups

Abstract

We prove in this note that every separable infinite dimensional complex Fréchet space different from $\omega$, the countably infinite product of lines, admits a topologically mixing analytic uniformly continuous semigroup of operators. The study of the existence of transitive semigroups on $\omega$, and on its predual $\varphi$ is also considered.