5. Functionals and Dual Spaces

Chapters in this book

1. Frontmatter I
2. Contents XI
3. List of Figures XV
4. Basic Notation XVII
5. 1. Choice Principles 1
6. 2. Hilbert Spaces 8
7. 3. Completeness, Completion and Dimension 36
8. 4. Linear Operators 53
9. 5. Functionals and Dual Spaces 66
10. 6. Fourier Series 78
11. 7. Fourier Transform 89
12. 8. Fixed Point Theorem 113
13. 9. Baire Category Theorem 126
14. 10. Uniform Boundedness Principle 137
15. 11. Open Mapping Theorem 143
16. 12. Closed Graph Theorem 147
17. 13. Hahn–Banach Theorem 151
18. 14. The Adjoint Operator 166
19. 15. Weak Topologies and Reflexivity 174
20. 16. Operators in Hilbert Spaces 183
21. 17. Spectral Theory of Operators on Hilbert Spaces 192
22. 18. Compactness 199
23. Bibliography 223
24. Index 225