Random sets and invariants for (type II) continuous tensor product systems of Hilbert spaces / / Volkmar Liebscher

• Record Nr.: UNINA9910829176703321
• Autore: Liebscher Volkmar <1965->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2009; ©2009
• ISBN: 1-4704-0536-9
• Descrizione fisica: 1 online resource (124 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 199, Number 930
• Disciplina: 515/.733
• Soggetti: Hilbert space; Random sets; Invariants; Calculus of tensors
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 199, Number 930 (first of 6 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""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""