  Continuity, compactness, the spectrum and ergodic properties of the
differentiation operator are investigated, when it acts in the Fr\'echet space
of all Dirichlet series that are uniformly convergent in all half-planes $\{s
\in \mathbb{C} \ | \ {\rm Re} s > \varepsilon \}$ for each $\varepsilon>0$. The
properties of the formal inverse of the differentiation are also investigated.
