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

Abstract

The paper discusses 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 * -algebra and ϕ is scalar-valued. In particular, we construct a suitable analogue of the Voiculescu's S-transform for this framework.