Topological vector spaces
With many examples and historical notes, this book provides a treatment of the Hahn-Banach theorem. It explores the theorem's connection with the axiom of choice, discusses the uniqueness of Hahn-Banach extensions, and includes a chapter on vector-valued Hahn-Banach theorems.
xvii, 610 pages : illustrations ; 25 cm.
9781584888666, 1584888660
144216834
1. Background
2. Commutative topological groups
3. Completeness
4. Topological vector spaces
5. Locally convex spaces and seminorms
6. Bounded sets
7. Hahn-Banach theorems
8. Duality
9. Krein-Milman and Banach-Stone
10. Vector- valued Hahn-Banach theorems
11. Barreled spaces
12. Inductive limits
13. Bornological spaces
14. Closed graph theorems
15. Reflexivity
16. Norm convexities and approximation