AN EXAMPLE OF A BOOLEAN-FREE TYPE CENTRAL LIMIT THEOREM
Anna Kula
Janusz Wysoczański
Abstract: We construct a product of Hilbert spaces and associated product of operators, which
generalizes the boolean and the free products and provides a model for new independence.
The related Central Limit Theorem is proved.
2000 AMS Mathematics Subject Classification: Primary: 60F05, 60B12; Secondary:
05A18, 06A07, 46L53. Keywords and phrases: Free independence, boolean independence,
noncommutative CLT, partially ordered sets.