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

1. Introduction. 2. Preliminaries. 3. Joint Free Distributions of Multi Semicircular Elements. 4. A C*-Probability Space of |Z|-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 . 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.