Accessible text covering core functional analysis topics in Hilbert and Banach spaces, with detailed proofs and 200 fully-worked exercises.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
James C. Robinson is a professor in the Mathematics Institute at the University of Warwick. He has been the recipient of a Royal Society University Research Fellowship and an Engineering and Physical Sciences Research Council (EPSRC) Leadership Fellowship. He has written six books in addition to his many publications in infinite-dimensional dynamical systems, dimension theory, and partial differential equations.
Inhaltsangabe
Part I. Preliminaries: 1. Vector spaces and bases 2. Metric spaces Part II. Normed Linear Spaces: 3. Norms and normed spaces 4. Complete normed spaces 5. Finite-dimensional normed spaces 6. Spaces of continuous functions 7. Completions and the Lebesgue spaces Lp(¿) Part III. Hilbert Spaces: 8. Hilbert spaces 9. Orthonormal sets and orthonormal bases for Hilbert spaces 10. Closest points and approximation 11. Linear maps between normed spaces 12. Dual spaces and the Riesz representation theorem 13. The Hilbert adjoint of a linear operator 14. The spectrum of a bounded linear operator 15. Compact linear operators 16. The Hilbert-Schmidt theorem 17. Application: Sturm-Liouville problems Part IV. Banach Spaces: 18. Dual spaces of Banach spaces 19. The Hahn-Banach theorem 20. Some applications of the Hahn-Banach theorem 21. Convex subsets of Banach spaces 22. The principle of uniform boundedness 23. The open mapping, inverse mapping, and closed graph theorems 24. Spectral theory for compact operators 25. Unbounded operators on Hilbert spaces 26. Reflexive spaces 27. Weak and weak-* convergence Appendix A. Zorn's lemma Appendix B. Lebesgue integration Appendix C. The Banach-Alaoglu theorem Solutions to exercises References Index.
Part I. Preliminaries: 1. Vector spaces and bases 2. Metric spaces Part II. Normed Linear Spaces: 3. Norms and normed spaces 4. Complete normed spaces 5. Finite-dimensional normed spaces 6. Spaces of continuous functions 7. Completions and the Lebesgue spaces Lp(¿) Part III. Hilbert Spaces: 8. Hilbert spaces 9. Orthonormal sets and orthonormal bases for Hilbert spaces 10. Closest points and approximation 11. Linear maps between normed spaces 12. Dual spaces and the Riesz representation theorem 13. The Hilbert adjoint of a linear operator 14. The spectrum of a bounded linear operator 15. Compact linear operators 16. The Hilbert-Schmidt theorem 17. Application: Sturm-Liouville problems Part IV. Banach Spaces: 18. Dual spaces of Banach spaces 19. The Hahn-Banach theorem 20. Some applications of the Hahn-Banach theorem 21. Convex subsets of Banach spaces 22. The principle of uniform boundedness 23. The open mapping, inverse mapping, and closed graph theorems 24. Spectral theory for compact operators 25. Unbounded operators on Hilbert spaces 26. Reflexive spaces 27. Weak and weak-* convergence Appendix A. Zorn's lemma Appendix B. Lebesgue integration Appendix C. The Banach-Alaoglu theorem Solutions to exercises References Index.
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