An Introduction to Hilbert Space and Quantum Logic

1. Experiments, Measure, and Integration.- A. Measures.- B. Integration.- 2. Hilbert Space Basics.- Inner product space, norm, orthogonality, Pythagorean theorem, Bessel and Cauchy-Schwarz and triangle inequalities, Cauchy sequences, convergence in norm, completeness, Hilbert space, summability, bases, dimension..- 3. The Logic of Nonclassical Physics.- A. Manuals of Experiments and Weights.- B. Logics and State Functions.- 4. Subspaces in Hilbert Space.- Linear manifolds, closure, subspaces, spans, orthogonal complements, the subspace logic, finite projection theorem, compatibility of subspaces..- 5. Maps on Hilbert Spaces.- A. Linear Functional and Function Spaces.- B. Projection Operators and the Projection Logic.- 6. State Space and Gleason’s Theorem.- A. The Geometry of State Space.- B. Gleason’s Theorem.- 7. Spectrality.- A. Finite Dimensional Spaces, the Spectral Resolution Theorem.- B. Infinite Dimensional Spaces, the Spectral Theorem.- 8. The Hilbert Space Model for Quantum Mechanics and the EPR Dilemma.- A. A Brief History of Quantum Mechanics.- B. A Hilbert Space Model for Quantum Mechanics.- C. The EPR Experiment and the Challenge of the Realists.- Index of Definitions.