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Lax, Peter D.
Functional analysis / Peter D. Lax.
— New York : Wiley-Interscience, c2002. xix, 580 p. ; 25 cm.
Incluye referencias bibliográficas e índice.
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.
ISBN 0471556041
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