I know that there exist Ito formulae to understand $ f(X), $ where $f: H\rightarrow \mathbb{R}$ is sufficiently nice, $H$ is a Hilbert space and $X$ is an $H$-valued semi-martingale.

However I'm wondering if there is a generalization or analogue for $f: H \mapsto \tilde{H}$, sufficiently nice operators between Hilbert spaces? I haven't been able to find anything, any references in the right direction are appreciated!