Click here to see the Errata 2nd Edition - Revised

Click here to see the Errata 2nd Edition

Click here to see the Errata 1st Editon

Introduction to Functional Analysis - Second Edition (C. R. de Oliveira; February/2008)

 

Contents (about 215 pages)

1. Normed Spaces

2. Compactness and Completion

2.1 Compactness and Dimension

2.2 Completion of Normed Spaces

3. Linear Operators

3.1 Separable Spaces

3.2 Linear Operators

4. Bounded Operators and Dual Space

5. Banach Fixed Point

6. Baire Category Theorem

7. Uniform Boundedness Principle

8. Open Mapping Theorem

9. Closed Graph Theorem

10. Hahn-Banach Theorem

10.1 Zorn Lemma

10.2 Hahn-Banach

11. Proof of Hahn-Banach

12. Applications of Hahn-Banach Theorem

13. Adjoint Operators in Normed Spaces

14. Weak Convergence

15. Weak Topologies

15.1 Weak Topologies

15.2 Alaoglu Theorem

16. Reflexive Spaces and Sequential Compactness

17. Hilbert Spaces

17.1 Inner Product

17.2 Orthogonality

18. Orthogonal Projection

18.1 Parallelogram Rule

18.2 Orthogonal Projection

19. Riesz Representation in Hilbert Spaces

19.1 Riesz Representation

19.2 Hilbert Adjoint and Lax-Milgram

20. Self-Adjoint Operators

21. Orthonormal Bases

22. Fourier Series

22.1 Fourier Series

22.2 Integration in Hilbert Spaces

23. Operations in Banach Spaces

23.1 Direct Sum

23.2 Quotient Space

24. Compact Operators

25. Compact Operators in Hilbert Spaces

26. Hilbert-Schmidt Operators

27. Spectrum

28. Spectral Classification

29. Spectrum of Self-Adjoint Operators

30. Spectrum of Compact Operators

30.1 Compact Operators

30.2 Normal Compact Operators

 


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