I Fundamentals of Banach Algebras and C*-Algebras. - 0. Introduction. - 1. Banach Algebras. - 2. Spectrum and Functional Calculus. - 3. Gelfand Representation of Abelian Banach Algebras. - 4. Spectrum and Functional Calculus in C*-Algebras. - 5. Continuity of Homomorphisms. - 6. Positive Cones of C*-Algebras. - 7. Approximate Identities in C*-Algebras. - 8. Quotient Algebras of C*-Algebras. - 9. Representations and Positive Linear Functional. - 10. Extreme Points of the Unit Ball of a C*-Algebra. - 11. Finite Dimensional C*-Algebras. - Notes. - Exercises. - II Topologies and Density Theorems in Operator Algebras. - 0. Introduction. - 1. Banach Spaces of Operators on a Hilbert Space. - 2. Locally Convex Topologies in ?(?). - 3. The Double Commutation Theorem of J. von Neumann. - 4. Density Theorems. - Notes. - III Conjugate Spaces. - 0. Introduction. - 1. Abelian Operator Algebras. - 2. The Universal Enveloping von Neumann Algebra of a C*-Algebra. - 3. W*-Algebras. - 4. The Polar Decomposition and the Absolute Value of Functionals. - 5. Topological Properties of the Conjugate Space. - 6. Semicontinuity in the Universal Enveloping von Neumann Algebra*. - Notes. - IV Tensor Products of Operator Algebras and Direct Integrals. - 0. Introduction. - 1. Tensor Product of Hilbert Spaces and Operators. - 2. Tensor Products of Banach Spaces. - 3. Completely Positive Maps. - 4. Tensor Products of C*-Algebras. - 5. Tensor Products of W*-Algebras. - Notes. - 6. Integral Representations of States. - 7. Representation of L2(??) ? ? L1(??) ?y? * and L(??) ?? ?. - 8. Direct Integral of Hubert Spaces Representations and von Neumann Algebras. - Notes. - V Types of von Neumann Algebras and Traces. - 0. Introduction. - 1. Projections and Types of von Neumann Algebras. - 2. Traces on von Neumann Algebras. -Notes. - 3. Multiplicity of a von Neumann Algebra on a Hilbert Space. - 4. Ergodic Type Theorem for von Neumann Algebras*. - 5. Normality of Separable Representations*. - 6. The Borel Spaces of von Neumann Algebras. - 7. Construction of Factors of Type II and Type III. - Notes. - Appendix Polish Spaces and Standard Borel Spaces. - Monographs. - Papers. - Notation Index. Language: English