Functional analysis / Peter D. Lax

Includes bibliographical references and index

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 inegral 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