Topics in Banach Space Theory

• Κύριοι συγγραφείς: Albiac, Fernando (Συγγραφέας), Kalton, Nigel J. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Έκδοση: 2nd ed. 2016.
• Σειρά: Graduate Texts in Mathematics, 233
• Θέματα: Mathematics.; Functional analysis.; Functional Analysis.

This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second ed...

Πίνακας περιεχομένων:

• 1. Bases and Basic Sequences
• 2. The Classical Sequence Spaces
• 3. Special Types of Bases
• 4. Banach Spaces of Continuous Functions
• 5. L_{1}(\mu )-Spaces and \mathcal C(K)-Spaces
• 6. The Spaces L_{p} for 1\le p<\infty
• 7. Factorization Theory
• 8. Absolutely Summing Operators
• 9. Perfectly Homogeneous Bases and Their Applications
• 10. Greedy-type Bases
• 11. \ell _p-Subspaces of Banach Spaces
• 12. Finite Representability of \ell _p-Spaces
• 13. An Introduction to Local Theory
• 14. Nonlinear Geometry of Banach Spaces
• 15. Important Examples of Banach Spaces
• Appendix A Normed Spaces and Operators
• Appendix B Elementary Hilbert Space Theory
• Appendix C Duality in L_{p}(\mu ): H\"older's inequality related results
• Appendix D Main Features of Finite-Dimensional Spaces
• Appendix E Cornerstone Theorems of Functional Analysis
• Appendix F Convex Sets and Extreme Points
• Appendix G The Weak Topologies
• Appendix H Weak Compactness of Sets and Operators
• Appendix I Basic probability in use
• Appendix J Generalities on Ultraproducts
• Appendix K The Bochner Integral abridged
• List of Symbols
• References
• Index.