03671nam 2200625 450 991048039450332120170816143246.01-4704-0536-9(CKB)3360000000465114(EBL)3114042(SSID)ssj0000889169(PQKBManifestationID)11478752(PQKBTitleCode)TC0000889169(PQKBWorkID)10875487(PQKB)11317683(MiAaPQ)EBC3114042(PPN)195418190(EXLCZ)99336000000046511420150415h20092009 uy 0engur|n|---|||||txtccrRandom sets and invariants for (type II) continuous tensor product systems of Hilbert spaces /Volkmar LiebscherProvidence, Rhode Island :American Mathematical Society,2009.©20091 online resource (124 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 199, Number 930"Volume 199, Number 930 (first of 6 numbers)."0-8218-4318-4 Includes bibliographical references.""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""Memoirs of the American Mathematical Society ;Volume 199, Number 930.Hilbert spaceRandom setsInvariantsCalculus of tensorsElectronic books.Hilbert space.Random sets.Invariants.Calculus of tensors.515/.733Liebscher Volkmar1965-904405MiAaPQMiAaPQMiAaPQBOOK9910480394503321Random sets and invariants for (type II) continuous tensor product systems of Hilbert spaces2022182UNINA