On the S-transform over a Banach algebra
arXiv:math/0501083
Abstract
The S-transform is shown to satisfy a specific twisted multiplicativity property for free random variables in a B-valued Banach noncommutative probability space, for an arbitrary unital complex Banach algebra B. Also, a new proof of the additivity of the R-transform in this setting is given.
16 pages. The revised version includes a new proof of additivity of the R-transform, as well as some minor corrections