2015/12/20 by Ken Dykema, Dykema, Ken
Mathematics · #16W60 #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA) #math.OA #math.RA #msc:16W60
paper · pdf · doi:10.48550/arxiv.1512.06323
This paper is withdrawn, because the results on canonical random variables were essentially known. (See Nica, Shlyakhtenko, Speicher, IMRN, 2002.) The results on traciality and cumulants have been included in arXiv:1512.06321
arxiv created 2016/01/12 · arxiv updated 2016/01/13
In the algebraic theory of algebra-valued noncommutative probability spaces, for a unital algebra B, a mild reformulation of Speicher's noncrossing B-valued cumulants for random variables in these spaces is used to construct canonical random variables, acting on a Fock space over B, for arbitrary families of B-valued random variables. Also, a condition for traciality of a trace on B composed with the B-valued conditional expectation is given in terms of B-valued cumulants.