On universal products. (English) Zbl 0877.46044

Speicher, Roland

Voiculescu, Dan-Virgil (ed.), Free probability theory. Papers from a workshop on random matrices and operator algebra free products, Toronto, Canada, Mars 1995. Providence, RI: American Mathematical Society. Fields Inst. Commun. 12, 257-266 (1997).

Summary: We define a universal product by the requirements of associativity and a universal calculation rule for mixed moments and show that for unital algebras there are no other universal products than the tensor product and the reduced free product of Voiculescu. In the non-unital case one gets, in addition, only the Boolean product.
For the entire collection see [Zbl 0859.00025].

MSC:

46L51	Noncommutative measure and integration
46L53	Noncommutative probability and statistics
46L54	Free probability and free operator algebras

Keywords:

universal product; associativity; universal calculation rule for mixed moments; unital algebras; tensor product; reduced free product of Voiculescu; Boolean product