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

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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 < ∞
CHAPTER 7 Free-Probabilistic Information on Ӿ [sub(N)] Affected by Partial Isometries
CHAPTER 8 Application I. Shift Operators Acting on Ӿ[sub(∞)]
CHAPTER 9 Application II. The Circular Law
	9.1 CIRCULAR ELEMENTS
	9.2 DEFORMED CIRCULAR LAWS ON Ӿ[sub(N)] BY PARTIAL ISOMETRIES OF λ[sub(N)]
CHAPTER 10 Application III. Free Poisson Distributions
	10.1 FREE POISSON ELEMENTS
	10.2 DEFORMED FREE POISSON DISTRIBUTIONS ON Ӿ[sub(N)]
CHAPTER 11 Examples
	11.1 PARTIAL ISOMETRIES OF λ[sub(5)] ⊂ Λ[sub(5)] ON Ӿ[sub(5)]
	11.2 PARTIAL ISOMETRIES OF λ[sub(∞)] ⊂ Λ[sub(∞)] ON X[sub(∞)]
CHAPTER 12 The Group-Dynamical System Γ
	12.1 DYNAMICS ON X[sub(φ)]
	12.2 THE Γ-SEMICIRCULAR ∗-PROBABILITY SPACE X
	12.3 DISCUSSION
CHAPTER 13 On The Γ-Semicircular ∗-Probability Space X
	13.1 GENERATING FREE RANDOM VARIABLES OF X
	13.2 FREE-DISTRIBUTIONAL DATA ON X
	13.3 MORE ABOUT FREE-DISTRIBUTIONAL DATA ON X
CHAPTER 14 Operator-Theoretic Properties on X
	14.1 OPERATOR-THEORETIC PROPERTIES ON G
	14.2 OPERATOR-THEORETIC PROPERTIES OF FREE
REDUCED WORDS OF X IN G
	14.3 CERTAIN OPERATOR SUMS OF X
	14.4 FREE DISTRIBUTIONS OF SOME SELF-ADJOINT
OPERATORS
CHAPTER 15 Free Probability on X[sub(N)] = (Ӿ[sub(N)] ⊗[sub(C)] Λ[sub(N)], τ[sub(N)])
	15.1 BANACH ∗-PROBABILITY SPACES X[sub(N)]
	15.2 FREE-DISTRIBUTIONAL DATA ON X[sub(N)]
	15.3 FREE-HOMOMORPHIC RELATIONS ON {X[sub(N)]}[sub(N∈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