Free Random Variables: Free Distributions Dictated by the Semicircular Law is particularly concerned with operators which are not self-adjoint, but whose free distributions are dictated by the semicircular law. The book covers operator-theoretic properties and free-distributional data of such operators and investigates operator-algebraic structures induced by those operators.
Features
• Includes multiple examples and applications
• Suitable for postgraduates and researchers.
I Constructive Analysis of Free Random Variables Followed by the Semicircular Law 1 Introduction 2 Preliminaries 3 Free Distributions of Multi Semicircular Elements 4 A C∗-Probability Space Generated by |N|-Many Semicircular Elements 5 Free-Distributional Data on Xϕ 6 Certain Free-Isomorphisms on Xϕ 7 Free Random Variables followed by the Semicircular Law 8 Free Random Variables Followed by the Circular Law 9 Free Random Variables Followed by Free Poisson Distributions 10 Discussions 11 A Structure Theorem of Xτ 12 Certain Banach-Space Operators Acting on Xτ 13 A Group-Dynamical System (Z, Xτ , α) 14 More About Free-Distributional Data on X [Γ] II Free Random Variables followed by the Semicircular Law 15 Free Random Variables Followed By The Semicircular Law 16 On the Copies of the C∗-Probability Space Xτ 17 Finitely-Many Free Random Variables Governed by The
Semicircular Law 18 Generalization 19 Applications Bibliography
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