Analysis Now
Graduate students in mathematics, who want to travel light, will find this book invaluable; impatient young researchers in other fields will enjoy it as an instant reference to the highlights of modern analysis. Starting with general topology, it moves on to normed and seminormed linear spaces. From...
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1989, 1989
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| Edition: | 1st ed. 1989 |
| Series: | Graduate Texts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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