On the S-transform over a Banach algebra
Operator Algebras
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0501083,
title = {On the S-transform over a Banach algebra},
author = {Kenneth J. Dykema},
journal= {arXiv preprint arXiv:math/0501083},
year = {2007}
}
Comments
16 pages. The revised version includes a new proof of additivity of the R-transform, as well as some minor corrections