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 $$*$$… Click to show full abstract
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.
               
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