This book covers various topics related to direct integral theory, including Borel spaces, direct integral of Hilbert spaces and operators, direct integrals of representations, direct integrals and types of von Neumann algebras, and measures on the quasi-dual representations.
Preface
Chapter 1
Borel Spaces
1. Definitions
2. Borel Spaces and Functions
3. Borel spaces and Equivalence Relations
4. Borel spaces and Measures
Historical Comments
Chapter 2
Direct Integrals of Hilbert Spaces and Operators
5. Hilbert Space-Valued L²-Spaces
6. Operators on Hilbert Space-Valued L²-Spaces
7. Fields of Hilbert Spaces and Operators
8. The Construction of Coherences
9. Direct Integral Decompositions
10. Examples
Historical Comments
Chapter 3
Direct Integrals of Representations
11. Definitions and some Elementary Properties
12. Equivalence, Existence and Uniqueness of Direct Interal Decompositions
13. Maximal and Central Decompositions
14. Some Applications
15. Examples
Historical Comments
Chapter 4
Direct Integrals of von Neumann Algebras
16. Hausdorff Metrics
17. The Effros Borel Structure
18. Definitions and Some Elementary Properties
19. Some Further Properties
20. Examples
Historical Comments
Chapter 5
Direct Integrals and Types of Von Neumann Algebras
21. The Statements of Two Theorems
22. Partial Proof of Theorem 21.1
23. Proof of Theorem 21.2
24. Some Technical Lemmas
25. The Completion of the Proof of Theorem 21.1
Historical Comments
Chapter 6
Measures and Representations
26. The Dual and the quasi-daul
27. Measures on the Dual and Representations
28. Measures on the Quasi-dual and Representations
Historical Comments
Appendix A
Von Neumann Algebras
Appendix B
Representations of Involutive Banach Algebras
Appendix C
Representations of Locally Compact Groups
References
Index of Notation
Index
Biography
O.A Neilsen