Quantum Measure Theory [Paperback]

Preface.1: Introduction.2: Operator Algebras. 2.1. C*-Algebras. 2.2. Von Neumann Algebras. 2.3. Jordan Algebras And Ordered Structures.3: Gleason Theorem. 3.1. Reduction To Three-Dimensional Space. 3.2. Regularity Of Frame Functions On R3. 3.3. Boundedness Of Frame Functions. 3.4. Historical Remarks And Comments.4: Completeness Criteria. 4.1. Functiona1 Completeness Criteria. 4.2. Algebraic Completeness Criteria. 4.3. Measure Theoretic Completeness Criteria. 4.4. Historical Remarks And Comments.5: Generalized Gleason Theorem. 5.1. The Mackey-Gleason Problem. 5.2. Reduction To Scalar Quasi-Functionals. 5.3. Linear Extensions Of Measures On Type In Algebras. 5.4. Linear Extensions Of Measures On Infinite Algebras. 5.5. Linear Extensions Of Measures On Finite Algebras. 5.6. Historical Remarks And Comments.6: Basic Principles Of Quantum Measure Theory. 6.1. Boundedness Of Completely Additive Measures. 6.2. Yosida-Hewitt Decompositions Of Quantum Measures. 6.3. Convergence Theorems. 6.4. Historical Remarks And Comments.7: Applications Of Gleason Theorem. 7.1. Multiform Gleason Theorem And Decoherence. 7.2. Velocity Maps And Derivations. 7.3. Approximate Hidden Variables. 7.4. Historical Remarks And Comments.8: Orthomorphisms Of Projections. 8.1. Orthomorphisms Of Projection Lattices. 8.2. Countable Additivity Of *-Homomorphisms. 8.3. Historical Remarks And Comments.9: Restrictions And Extensions Of States. 9.1. Restriction Properties Of Pure States. 9.2. Gleason Type Theorems For Quantum Logics. 9.3. Historical Remarks And Comments.10: Jauch-Piron States. 10.1. Basic Properties Of Jauch States. 10.2. Nonsingularity Of Jauch-Piron States. 10.3. Countable Additivity Of States. 10.4. Historical Remarks And Comments.11: Independence Of Quantum Systems. 11.1. Independence In Classical And Quantum Theory. 11.2. Independence Of C*-Algebras. 11.3. Independence Of Von Neumann Algebras. 11.4. Historical Remarks And Comments.Bibliography.Index.Springer Book Archives