Markus Haase, Delft University of Technology, Delft, The Netherlands
+ Read more• Preface 14
• Chapter 1. Inner product spaces 20
• Chapter 2. Normed spaces 34
• Chapter 3. Distance and approximation 56
• Chapter 4. Continuity and compactness 74
• Chapter 5. Banach spaces 98
• Chapter 6. The contraction principle 112
• Chapter 7. The Lebesgue spaces 126
• Chapter 8. Hilbert space fundamentals 148
• Chapter 9. Approximation theory and Fourier analysis 166
• Chapter 10. Sobolev spaces and the Poisson problem 196
• Chapter 11. Operator theory I 212
• Chapter 12. Operator theory II 230
• Chapter 13. Spectral theory of compact self-adjoint operators 250
• Chapter 14. Applications of the spectral theorem 266
• Chapter 15. Baire’s theorem and its consequences 280
• Chapter 16. Duality and the Hahn-Banach theorem 296
• Historical remarks 324
• Appendix A. Background 330
• Appendix B. The completion of a metric space 352
• Appendix C. Bernstein’s proof of Weierstrass’ theorem 358
• Appendix D. Smooth cutoff functions 362
• Appendix E. Some topics from Fourier analysis 364
• Appendix F. General orthonormal systems 370
• Bibliography 374
• Symbol Index 378
• Subject Index 380
• Author Index 390
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