The paper addresses several problems left open by P. Biane, F. Goodman and A. Nica [Trans. Amer. Math. Soc. 355 (2003)]. The main result is that a type B non-commutative probability space can be studied in the framework of freeness with amalgamation. This view allows easy ways of constructing a version of the S-transform as well as proving analogues to the Central Limit Theorem and Poisson Limit Theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-2-11,
author = {Mihai Popa},
title = {Freeness with amalgamation, limit theorems and S-transform in non-commutative probability spaces of type B},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {319-329},
zbl = {1213.46063},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-2-11}
}
Mihai Popa. Freeness with amalgamation, limit theorems and S-transform in non-commutative probability spaces of type B. Colloquium Mathematicae, Tome 120 (2010) pp. 319-329. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-2-11/