| General Theory | |
| Definitions of C*-Algebras and W*-Algebras | p. 1 |
| Commutative C*-Algebras | p. 3 |
| Stonean Spaces | p. 6 |
| Positive Linear Functions on a C*-Algebra | p. 7 |
| Positive Linear Functionals on a C*-Algebra | p. 9 |
| Extreme Points in the Unit Sphere of a C*-Algebra | p. 10 |
| The Weak Topology on a W*-Algebra | p. 14 |
| Various Topologies on a W*-Algebra | p. 19 |
| Kaplansky's Density Theorem | p. 22 |
| Ideals in a W*-Algebra | p. 24 |
| Spectral Resolution of Self-Adjoint Elements in a W*-Algebra | p. 26 |
| The Polar Decomposition of Elements of a W*-Algebra | p. 27 |
| Linear Functionals on a W*-Algebra | p. 28 |
| Polar Decomposition of Linear Functionals on a W*-Algebra | p. 31 |
| Concrete C*-Algebras and W*-Algebras | p. 33 |
| The Representation Theorems for C*-Algebras and W*-Algebras | p. 40 |
| The Second Dual of a C*-Algebra | p. 42 |
| Commutative W*-Algebras | p. 45 |
| The C*-Algebra C(H) of all Compact Linear Operators on a Hilbert Space H | p. 46 |
| The Commutation Theorem of von Neumann | p. 48 |
| *-Representations of C*-Algebras, 1 | p. 50 |
| Tensor Products of C*-Algebras and W*-Algebras | p. 58 |
| The Inductive Limit and Infinite Tensor Product of C*-Algebras | p. 70 |
| Radon-Nikodym Theorems in W*-Algebras | p. 75 |
| Classification of W*-Algebras | |
| Equivalence of Projections and the Comparability Theorem | p. 79 |
| Classification of W*-Algebras | p. 83 |
| Type I W*-Algebras | p. 87 |
| Finite W*-Algebras | p. 89 |
| Traces and Criterions of Types | p. 95 |
| Types of Tensor Products of W*-Algebras | p. 98 |
| *-Representations of C*-Algebras and W*-Algebras, 2 | p. 102 |
| The Commutation Theorem of Tensor Products | p. 108 |
| Spatial Isomorphisms of W*-Algebras | p. 111 |
| Decomposition Theory | |
| Decompositions of States (Non-Separable Cases) | p. 121 |
| Reduction Theory (Space-Free) | p. 131 |
| Direct Integral of Hilbert Spaces | p. 137 |
| Decomposition of States (Separable Cases) | p. 140 |
| Central Decomposition of States (Separable Cases) | p. 146 |
| Special Topics | |
| Derivations and Automorphisms of C*-Algebras and W*-Algebras | p. 153 |
| Examples of Factors, 1 (General Construction) | p. 171 |
| Examples of Factors, 2 (Uncountable Families of Types II[subscript 1], [actual symbol not reproducible] and III | p. 183 |
| Examples of Factors, 3 (Other Results and Problems) | p. 202 |
| Global W*-Algebras (Non-Factors) | p. 216 |
| Type I C*-Algebras | p. 219 |
| On a Stone-Weierstrass Theorem for C*-Algebras | p. 236 |
| Bibliography | p. 243 |
| Subject Index | p. 251 |
| List of Symbols | p. 255 |
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