"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"--
This book 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.
1. Introduction.
2. Preliminaries.
3. Joint Free Distributions of Multi Semicircular Elements.
4. A C*-Probability Space of |?|-Many Semicircular Elements.
5. C*-Probability Spaces (?N ; ?N).
6. Adjointable Banach-Space Operators Acting on ?N.
7. Free-Probabilistic Information on ?N Affected by Partial Isometries.
8. Application I. Shift Operators Acting on ?8.
9. Application II. The Circular Law.
10. Application III. Free Poisson Distributions.
11. Examples.
12. The Group Dynamical System ?.
13. On the ?-Semicircular *-Probability Space X.
14. Operator-Theoretic Properties on X. Free Probability on ?N = (?N ?C ^N; TN).
16. Operator-Theoretic Properties on ?N.
Ilwoo Cho is currently professor at St. Ambrose University, Iowa. Dr Cho earned his PhD in Mathematics from University of Iowa in 2005 and his masters degree from Sungkyunkwan University in 1999. Dr Cho's research interests include free probability, operator algebra and theory, combinatorics, and groupoid dynamical systems.
