Geometric functional analysis and its applications/
R. B. Holmes
- New York : Springer, 2013.
- 246p. : 24cm.
Includes index and references.
I Convexity in Linear Spaces.- 1. Linear Spaces.- 2. Convex Sets.- 3. Convex Functions.- 4. Basic Separation Theorems.- 5. Cones and Orderings.- 6. Alternate Formulations of the Separation Principle.- 7. Some Applications.- 8. Extremal Sets.- Exercises.- II Convexity in Linear Topological Spaces.- 9. Linear Topological Spaces.- 10. Locally Convex Spaces.- 11. Convexity and Topology.- 12. Weak Topologies.- 13. Extreme Points.- 14. Convex Functions and Optimization.- 15. Some More Applications.- Exercises.- III Principles of Banach Spaces.- 16. Completion, Congruence, and Reflexivity.- 17. The Category Theorems.- 18. The Smulian Theorems.- 19. The Theorem of James.- 20. Support Points and Smooth Points.- 21. Some Further Applications.- Exercises.- IV Conjugate Spaces and Universal Spaces.- 22. The Conjugate of C(?, ?).- 23. Properties and Characterizations of Conjugate Spaces.- 24. Isomorphism of Certain Conjugate Spaces.- 25. Universal Spaces.-