On the S-transform over a Banach algebra

摘要

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. (C) 2005 Elsevier Inc. All rights reserved.