Table of Contents: “…Introduction -- Part I Co(X) and B(H): Classical physics on a finite phase space -- Quantum mechanics on a finite-dimensional Hilbert space -- Classical physics on a general phase space -- Quantum physics on a general Hilbert space -- Symmetry in quantum mechanics -- Part II Between Co(X) and B(H): Classical models of quantum mechanics -- Limits: Small hbar -- Limits: large N -- Symmetry in algebraic quantum theory -- Spontaneous Symmetry Breaking -- The Measurement Problem -- Topos theory and quantum logic -- Appendix A: Finite-dimensional Hilbert spaces -- Appendix B: Basic functional analysis -- Appendix C: Operator algebras -- Appendix D: Lattices and logic -- Appendix E: Category theory and topos theory -- References.…”
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Subjects: “…Functional analysis Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$- ) algebras, etc.) …”

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Table of Contents: “…Introduction -- Number and operations -- Algebra, patterns, and functions -- Geometry -- Measurement -- Data analysis and probability.…”

Table of Contents: “…Introduction -- Number and operations -- Algebra-patterns and functions -- Geometry -- Measurement -- Data analysis and probability.…”

Table of Contents: “…Z -- A case study: duality for Cantor sets -- Infinite products -- The minimal eigenfunction -- Generalizations and applications -- Pyramids and operators -- Pairs of representations of the Cuntz algebras O[subscript n], and their application to multiresolutions -- Appendices: Polyphase matrices and the operator algebra O[subscript N] -- Afterword.…”

Table of Contents: “…Ferreira -- Solution estimates for autonomous differential equations in a Hilbert space with several delays / Michael Gil' -- Controllability of quasi-linear evolution differential system in a separable Banach space / Bheeman Radhakrishnan -- Derivations of operator algebras on hypercomplex Hilbert spaces and related modules / S.V. …”
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Table of Contents: “…Introduction -- Spaces of Test Functions -- Schwartz Distributions -- Calculus for Distributions -- Distributions as Derivatives of Functions -- Tensor Products -- Convolution Products -- Applications of Convolution -- Holomorphic Functions -- Fourier Transformations -- Distributions as Boundary Values of Analytic Functions -- Other Spaces of Generalized Functions -- Sobolev Spaces -- Hilbert Spaces: A Brief Historical Introduction -- Inner Product Spaces and Hilbert Spaces -- Geometry of Hilbert Spaces -- Separable Hilbert Spaces -- Direct Sums and Tensor Products -- Topological Aspects -- Linear Operators -- Quadratic Forms -- Bounded Linear Operators -- Special Classes of Linear Operators -- Elements of Spectral Theory -- Compact Operators -- Hilbert-Schmidt and Trace Class Operators -- The Spectral Theorem -- Some Applications of the Spectral Representation -- Spectral Analysis in Rigged Hilbert Spaces -- Operator Algebras and Positive Mappings -- Positive Mappings in Quantum Physics -- Introduction -- Direct Methods in the Calculus of Variations -- Differential Calculus on Banach Spaces and Extrema of Functions -- Constrained Minimization Problems (Method of Lagrange Multipliers) -- Boundary and Eigenvalue Problems -- Density Functional Theory of Atoms and Molecules -- Appendices -- Index.  .…”
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Table of Contents: “…2.3.1 The Representation -- 2.3.2 The Representation -- 2.3.3 Inequivalence of -- 2.3.4 Other Inequivalent Representations -- 2.4 Operator Algebraic Interlude -- 2.4.1 Algebras: Basic Definitions and Properties -- 2.4.2 States and Representations -- 2.4.3 Automorphisms and Antiautomorphisms -- 2.4.4 Tensor Products -- 2.4.5 Quantum Dynamical Systems -- 2.4.6 Derivations of *-Algebras and Generators of Dynamical Groups -- 2.5 Algebraic Formulation of Infinite Systems -- 2.5.1 The General Scheme -- 2.5.2 Construction of the Lattice Model -- 2.5.3 Construction of the Continuum Model…”
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