On the multiplication of operator-valued c-free random variables

We discuss some results concerning the multiplication of non-commutative random variables that are c-free with respect to a pair $( \Phi, \varphi)$, where $\Phi$ is a linear map with values in some Banach or C$^\ast$-algebra and $\varphi$ is scalar-valued. In particular, we construct a suitable analogue of the Voiculescu's $S$-transform for this framework.