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
Author(s): Ilwoo Cho
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Publisher: CRC Press/Chapman & Hall
Year: 2022
Language: English
Pages: 228
City: Boca Raton
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 < ∞
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
