Free-Homomorphic Relations on Banach *-Probability Spaces Generated by Semicircular Elements Induced by Natural Numbers

摘要

In this paper, we study how an arbitrary natural number, greater than 1, induces a finite free semicircular family, and the corresponding Banach *-probability space. And then certain *-homomorphisms acting on such Banach *-probability spaces are considered. In particular, we are interested in cases where such *-homomorphisms preserve free-distributional data among them.