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 $( Φ, φ)$, where $Φ$ is a linear map with values in some Banach or C$^\ast$-algebra and $φ$ is scalar-valued. In particular, we construct a suitable analogue of the Voiculescu's $S$-transform for this framework.

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