Banach-Space Operators On C*-Probability Spaces Generated by Multi Semicircular Elements

Description

Banach-Space Operators On C*-Probability Spaces Generated by Multi Semicircular Elements introduces new areas in operator theory and operator algebra, in connection with free probability theory.In particular, the book considers projections and partial isometries distorting original free-distributional data on the C∗-probability spaces. Features Suitable for graduate students and professional researchers in operator theory and/or analysis. Numerous applications in related scientific fields and areas Cover Half Title Series Page Title Page Copyright Page Table of Contents AUTHOR CHAPTER 1 Introduction 1.1 MOTIVATION AND BACKGROUND 1.2 OVERVIEW CHAPTER 2 Preliminaries 2.1 FREE PROBABILITY 2.2 SEMICIRCULAR ELEMENTS 2.3 GROUP DYNAMICAL SYSTEMS AND CROSSED PRODUCT ALGEBRAS CHAPTER 3 Joint Free Distributions of Multi Semicircular Elements CHAPTER 4 A C[sup(∗)]-Probability Space of |Z|-Many Semicircular Elements CHAPTER 5 C[sup(∗)]-Probability Spaces (Ӿ[sub(N)], φ N) 5.1 FREE-DISTRIBUTIONAL DATA ON Ӿ[sub(N)] 5.2 RESTRICTED ACTIONS α[sub(N)] OF λ ON Ӿ[sub(N)] 5.3 ACTION OF Λ[sub(N)] ON Ӿ[sub(N)] 5.4 FREE-HOMOMORPHIC RELATIONS ON {Ӿ[sub(N)]}[sub(N∈N∞>1)] CHAPTER 6 Adjointable Banach-Space Operators Acting on Ӿ[sub(N)] 6.1 PROJECTIONS OF Λ[sub(N)] 6.2 PARTIAL ISOMETRIES ON Ӿ[sub(N)] 6.3 FREE-DISTRIBUTIONAL DATA AFFECTED BY PARTIAL ISOMETRIES 6.4 PARTIAL ISOMETRIES OF Λ[sub(N)] FOR N 1)] CHAPTER 16 Operator-Theoretic Properties on X[sub(N)] 16.1 OPERATOR-THEORETIC PROPERTIES ON Λ[sub(N)] 16.2 OPERATOR-THEORETIC PROPERTIES OF X[sup(S)][sub(J)] ⊗ T IN X[sub(N)] 16.3 OPERATOR-THEORETIC PROPERTIES OF W ⊗ T IN X[sub(N)] CHAPTER 17 Summary Bibliography Index