A Banach Algebra Approach To Amalgamated R- and S-transforms

Abstract

We give a Banach algebra approach to the additiveness property of Voiculescu's amalgamated R-transform. We also define an amalgamated S-transform and prove that it is multiplicative on products of amalgamated free random variables when the algebra of amalgamation is commutative.

22 pages

Cited by in corpus (2)

• Multilinear function series and transforms in free probability theory
• On the S-transform over a Banach algebra