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# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Freeness with amalgamation, limit theorems and $S$-transform in non-commutative probability spaces of type B

### Tom 120 / 2010

Colloquium Mathematicum 120 (2010), 319-329 MSC: 46L54, 46L53. DOI: 10.4064/cm120-2-11

#### Streszczenie

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.

#### Autorzy

• Mihai PopaCenter for Advanced Studies in Mathematics
Ben Gurion University of the Negev
P.O.B. 653
Be'er Sheva 84105, Israel
and
Institute of Mathematics “Simion Stoilow”