Authors:
1991 Mathematics Subject Classification :
- 60B12 Limit theorem for vector-valued random variables
- 46L50 Self-adjoint operator algebras
Abstract: Let 
be a real symmetric probability measure, with moments of
each order; we prove the existence of an unital *-algebra 
, with a state 
, and of a family
of self-adjoint,
weakly independent and symmetrically distributed elements of , such that all the moments of
converge to
those of when 
goes to the infinity. The algebra is realized with the help
of a generalization of the concepts of reduced free product due to
D. Voiculescu and of reduced 
-product due to M. Bozejko and R. Speicher.
keywords: Central Limit Theorem, Reduced Free
Product.