## ABSTRACT

** 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.

1. Introduction. 2. Preliminaries. 3. Joint Free Distributions of Multi Semicircular Elements. 4. A C*-Probability Space of |Ƶ|-Many Semicircular Elements. 5. C*-Probability Spaces (ЖN ; ɬN). 6. Adjointable Banach-Space Operators Acting on ЖN. 7. Free-Probabilistic Information on ЖN Affected by Partial Isometries. 8. Application I. Shift Operators Acting on Ж∞. 9. Application II. The Circular Law. 10. Application III. Free Poisson Distributions. 11. Examples. 12. The Group Dynamical System ſ. 13. On the ſ-Semicircular *-Probability Space X. 14. Operator-Theoretic Properties on X. Free Probability on ЖN = (ЖN ʘC ^N; TN). 16. Operator-Theoretic Properties on ЖN.