Book:Peter D. Lax/Functional Analysis

Subject Matter

 * Functional Analysis

Contents
Foreword


 * 1. Linear Spaces


 * 2. Linear Maps


 * 3. The Hahn-Banach Theorem


 * 4. Applications of the Hahn-Banach Theorem


 * 5. Normed Linear Spaces


 * 6. Hilbert Space


 * 7. Applications of Hilbert Space Results


 * 8. Duals of Normed Linear Spaces


 * 9. Applications of Duality


 * 10. Weak Convergence


 * 11. Applications of Weak Convergence


 * 12. The Weak and Weak* Topologies


 * 13. Locally Convex Topologies and the Krein-Milman Theorem


 * 14. Examples of Convex Sets and Their Extreme Points


 * 15. Bounded Linear Maps


 * 16. Examples of Bounded Linear Maps


 * 17. Banach Algebras and their Elementary Spectral Theory


 * 18. Gelfand's Theory of Commutative Banach Algebras


 * 19. Applications of Gelfand's Theory of Commutative Banach Algebras


 * 20. Examples of Operators and Their Spectra


 * 21. Compact Maps


 * 22. Examples of Compact Operators


 * 23. Positive Compact Operators


 * 24. Fredholm's Theory of Integral Equations


 * 25. Invariant Subspaces


 * 26. Harmonic Analysis on a Halfline


 * 27. Index Theory


 * 28. Compact Symmetric Operators in Hilbert Space


 * 29. Examples of Compact Symmetric Operators


 * 30. Trace Class and Trace Formula


 * 31. Spectral Theory of Symmetric, Normal, and Unitary Operators


 * 32. Spectral Theory of Self-Adjoint Operators


 * 33. Examples of Self-Adjoint Operators


 * 34. Semigroups of Operators


 * 35. Groups of Unitary Operators


 * 36. Examples of Strongly Continuous Semigroups


 * 37. Scattering Theory


 * 38. A Theorem of Beurling

Texts


 * A. A Riesz-Kakutani representation theorem


 * B. Theory of distributions


 * C. Zorn's Lemma


 * Author Index


 * Subject Index