Fundamentals of the Theory of Operator Algebras Special Topics Advanced Theory—An Exercise Approach

These volumes are companions to the treatise; "Fundamentals of the Theory of Operator Algebras," which appeared as Volume 100 - I and II in the series, Pure and Applied Mathematics, published by Academic Press in 1983 and 1986, respectively. As stated in the preface to those volumes, "Their primary goal is to teach the sub­ ject and lead the reader to the point where the vast recent research literature, both in the subject proper and in its many applications, becomes accessible." No attempt was made to be encyclopcedic; the choice of material was made from among the fundamentals of what may be called the "classical" theory of operator algebras. By way of supplementing the topics selected for presentation in "Fundamentals," a substantial list of exercises comprises the last section of each chapter. An equally important purpose of those exer­ cises is to develop "hand-on" skills in use ofthe techniques appearing in the text. As a consequence, each exercise was carefully designed to depend only on the material that precedes it, and separated into segments each of which is realistically capable of solution by an at­ tentive, diligent, well-motivated reader.

6. Comparison Theory of Projections — Exercises and Solutions.- 7. Normal States and Unitary Equivalence of von Neumann Algebras — Exercises and Solutions.- 8. The Trace — Exercises and Solutions.- 9. Algebra and Commutant — Exercises and Solutions.- 10. Special Representations of C*-Algebras — Exercises and Solutions.- 11. Tensor Products — Exercises and Solutions.- 12. Approximation by Matrix Algebras — Exercises and Solutions.- 13. Crossed Products — Exercises and Solutions.- 14. Direct Integrals and Decompositions — Exercises and Solutions.