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

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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.

Keywords: probability spaces; free homomorphic; relations banach; probability; banach probability; homomorphic relations

Journal Title: Complex Analysis and Operator Theory
Year Published: 2021

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