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

Abstract

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

second version, with less typos and some corrections

References in corpus (2)

• Non-crossing linked partitions and multiplication of free random variables
• A Fock Space Model for Addition and Multiplication of C-free Random Variables