On the construction of free random variables
The aim of the paper is to investigate the construction of free families of random variables from an initial free family, in a tracial noncommutative probability space. The random variables in this initial free family are multiplied on the left and the right by certain operators from a \(*\)-algebra free from the entire family. Necessary and sufficient conditions are obtained in various cases of the considered problem, and some of them are inspired by similar results and notions comprised by \textit{A. Nica} and \textit{R. Speicher} [Am. J. Math. 118, No. 4, 799-837 (1996; Zbl 0856.46035)].
multiplication by certain operators of a free family of random variables
tracial noncommutative probability space
scientific article; zbMATH DE number 1216762
scientific article