Functional analysis
Peter D. Lax.
New York : Wiley-Interscience, ©2002.
xix, 580 págs. ; 25 cm.
ISBN: 0471556041
Incluye referencias bibliográficas e índice.
Reseña: MathSciNet, 2003a:47001
Contenido
- 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 space
- 9. Applicaitons of duality
- 10. Weak sequential convergence
- 11. Applications of weak sequential convergence
- 12. The weak and weak* topologies in Banach spaces
- 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. Index theory
- 25. Invariant subspaces
- 26. Harmonic analysis on a halfline
- 27. Fredholm theory of integral equations
- 28. Spectral theory of compact, symmetric operators
- 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 selfadjoint operators
- 33. Examples of selfadjoint operators
- 34. Semigroups of operators
- 35. Groups of unitary operators
- 36. Examples of strongly continuous semigroups
- 37. Scattering theory
- 38. A theorem of Beurling
- Appendices: A. Riesz-Kakutani representation theorem; B. Theory of distributions; C. Zorn's lemma.
