2011/10/24 by D. Shlyakhtenko, Shlyakhtenko, D.
Mathematics · #46L54 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L54
paper · pdf · doi:10.48550/arxiv.1110.5127
arxiv created 2011/10/24 · arxiv updated 2011/10/25
We give an explicit realization of the η-convolution power of an A-valued distribution, as defined earlier by Anshelevich, Belinschi, Fevrier and Nica. If η:A→ A is completely positive and η\geqid, we give a short proof of positivity of the η-convolution power of a positive distribution. Conversely, if η\not\geqid, and s is large enough, we construct an s-tuple whose A-valued distribution is positive, but has non-positive η-convolution power.