Let $A$ be some algebra (infinite-dimensional) of analytic functions on $\mathbb{C}^n$, and $D$ be some derivation of $A$, i.e. $D(fg)=Df \cdot g + f \cdot Dg)$ (so A may be considered as a differential algebra).
When is this derivation continuous (in some natural topology on $A$)? Are there any useful sufficient conditions for the continuity of such derivations?