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Holmes,R. B.

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.-

ISBN: 146849371X

Subjects--Topical Terms:
Mathematics--Geometry.
Geometry.
Functional geometry.
Geometrical analysis.

Dewey Class. No.: 515.7 / HOL/G