Functional analysis / Peter D. Lax.
Editor: New York : Wiley-Interscience, c2002Descripción: xix, 580 p. ; 25 cmISBN: 0471556041Tema(s): Functional analysisOtra clasificación: 47-01 (46-01) Recursos en línea: Publisher description1. Linear spaces2. Linear maps3. The Hahn-Banach theorem4. Applications of the Hahn-Banach theorem5. Normed linear spaces6. Hilbert space7. Applications of Hilbert space results8. Duals of normed linear space9. Applicaitons of duality10. Weak sequential convergence11. Applications of weak sequential convergence12. The weak and weak* topologies in Banach spaces13. Locally convex topologies and the Krein-Milman theorem.14. Examples of convex sets and their extreme points15. Bounded linear maps16. Examples of bounded linear maps17. Banach algebras and their elementary spectral theory18. Gelfand's theory of commutative Banach algebras19. Applications of Gelfand's theory of commutative Banach algebras20. Examples of operators and their spectra21. Compact maps22. Examples of compact operators23. Positive compact operators24. Index theory25. Invariant subspaces26. Harmonic analysis on a halfline27. Fredholm theory of integral equations28. Spectral theory of compact, symmetric operators29. Examples of compact symmetric operators30. Trace class and trace formula31. Spectral theory of symmetric, normal and unitary operators32. Spectral theory of selfadjoint operators33. Examples of selfadjoint operators34. Semigroups of operators35. Groups of unitary operators36. Examples of strongly continuous semigroups37. Scattering theory38. A theorem of BeurlingAppendices: A. Riesz-Kakutani representation theorem; B. Theory of distributions; C. Zorn's lemma.
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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.
MR, 2003a:47001
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