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

chapter Chapter 1|4 pages

Introduction

chapter Chapter 2|4 pages

Preliminaries

chapter Chapter 5|19 pages

C ∗-Probability Spaces (𝔛 N , φN )

chapter Chapter 9|13 pages

Application II. The Circular Law

chapter Chapter 10|10 pages

Application III. Free Poisson Distributions

chapter Chapter 11|9 pages

Examples

chapter Chapter 12|6 pages

The Group-Dynamical System Γ

chapter Chapter 13|12 pages

On The Γ-Semicircular *-Probability Space 𝕏

chapter Chapter 14|27 pages

Operator-Theoretic Properties on 𝕏

chapter Chapter 16|15 pages

Operator-Theoretic Properties on 𝒳N

chapter Chapter 17|2 pages

Summary