Random Sets and Invariants for (Type II) Continuous Tensor Product Systems of Hilbert Spaces.

Intro -- Contents -- Chapter 1. Introduction -- Chapter 2. Basics -- Chapter 3. From Product Systems to Random Sets -- 3.1. Product Systems -- 3.2. Random Sets in Product Systems -- 3.3. Measure Types as Invariants -- 3.4. Measure Types Related to Units -- 3.5. Tensor Products (I) -- Chapter 4. From Random Sets to Product Systems -- 4.1. General Theory -- 4.2. Example 1: Finite Random Sets -- 4.3. Example 2: Countable Random Sets -- 4.4. Example 3: Random Cantor Sets -- 4.5. Tensor Products (II) -- 4.6. The map e [omitted] M[sup(e,u)] is surjective -- Chapter 5. An Hierarchy of Random Sets -- 5.1. Factorising Projections and Product Subsystems -- 5.2. Subsystems of e[sup(M)] -- 5.3. The Lattice of Stationary Factorising Measure Types -- Chapter 6. Direct Integral Representations -- 6.1. Random Sets and Direct Integrals -- 6.2. Direct Integrals in Product Systems -- 6.3. Characterisations of Type I Product Systems -- 6.4. Unitalising Type III Product Systems -- Chapter 7. Measurability in Product Systems: An Algebraic Approach -- 7.1. GNS-representations -- 7.2. Algebraic Product Systems and Intrinsic Measurable Structures -- 7.3. Product Systems of W*-Algebras -- 7.4. Product systems and Unitary Evolutions -- 7.5. Additional Results on Measurability -- Chapter 8. Construction of Product Systems from General Measure Types -- 8.1. General Results -- 8.2. Product Systems from Random Sets -- 8.3. Product Systems from Random Measures -- 8.4. Product Systems from Random Increment Processes -- Chapter 9. Beyond Separability: Random Bisets -- Chapter 10. An Algebraic Invariant of Product Systems -- Chapter 11. Conclusions and Outlook -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.