1st Edition

Direct Integral Theory

By O. A. Nielsen Copyright 1980
    184 Pages
    by CRC Press

    184 Pages
    by CRC Press

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    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