Analysis Now

1 General Topology. - 1. 1. Ordered Sets. - 1. 2. Topology. - 1. 3. Convergence. - 1. 4. Continuity. - 1. 5. Separation. - 1. 6. Compactness. - 1. 7. Local Compactness. - 2 Banach Spaces. - 2. 1. Normed Spaces. - 2. 2. Category. - 2. 3. Dual Spaces. - 2. 4. Seminormed Spaces. - 2. 5. w*-Compactness. - 3 Hilbert Spaces. - 3. 1. Inner Products. - 3. 2. Operators on Hilbert Space. - 3. 3. Compact Operators. - 3. 4. The Trace. - 4 Spectral Theory. - 4. 1. Banach Algebras. - 4. 2. The Gelfand Transform. - 4. 3. Function Algebras. - 4. 4. The Spectral Theorem I. - 4. 5. The Spectral Theorem II. - 4. 6. Operator Algebra. - 4. 7. Maximal Commutative Algebras. - 5 Unbounded Operators. - 5. 1. Domains Extensions and Graphs. - 5. 2. The Cayley Transform. - 5. 3. Unlimited Spectral Theory. - 6 Integration Theory. - 6. 1. Radon Integrals. - 6. 2. Measurability. - 6. 3. Measures. - 6. 4. LP-Aspaces. - 6. 5. Duality Theory. - 6. 6. Product Integrals. - List of Symbols. Language: English