Author | Bourbaki, Nicolas. author |
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Title | Topological Vector Spaces [electronic resource] : Chapters 1-5 / by Nicolas Bourbaki |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2003 |
Connect to | http://dx.doi.org/10.1007/978-3-642-61715-7 |
Descript | VII, 362 p. online resource |
I. โ Topological vector spaces over a valued division ring I. -- ยง 1. Topological vector spaces -- ยง 2. Linear varieties in a topological vector space -- ยง 3. Metrisable topological vector spaces -- Exercises of ยง 1 -- Exercises of ยง 2 -- Exercises of ยง 3 -- II. โ Convex sets and locally convex spaces II. -- ยง 1. Semi-norms -- ยง 2. Convex sets -- ยง 3. The Hahn-Banach Theorem (analytic form) -- ยง 4. Locally convex spaces -- ยง 5. Separation of convex sets -- ยง 6. Weak topologies -- ยง 7. Extremal points and extremal generators -- ยง 8. Complex locally convex spaces -- Exercises on ยง 2 -- Exercises on ยง 3 -- Exercises on ยง 4 -- Exercises on ยง 5 -- Exercises on ยง 6 -- Exercises on ยง 7 -- Exercises on ยง 8 -- III. โ Spaces of continuous linear mappings III. -- ยง 1. Bornology in a topological vector space -- ยง 2. Bornological spaces -- ยง 3. Spaces of continuous linear mappings -- ยง 4. The Banach-Steinhaus theorem -- ยง 5. Hypocontinuous bilinear mappings -- ยง 6. Borelโs graph theorem -- Exercises on ยง 1 -- Exercises on ยง 2 -- Exercises on ยง 3 -- Exercises on ยง 4 -- Exercises on ยง 5 -- Exercises on ยง 6 -- IV. โ Duality in topological vector spaces IV. -- ยง 1. Duality -- ยง 2. Bidual. Reflexive spaces -- ยง 3. Dual of a Frรฉchet space -- ยง 4. Strict morphisms of Frรฉchet spaces -- ยง 5. Compactness criteria -- Appendix. โ Fixed points of groups of affine transformations -- Exercises on ยง 1 -- Exercises on ยง 2 -- Exercises on ยง 3 -- Exercises on ยง 4 -- Exercises on ยง 5 -- Exercises on Appendix -- Table I. โ Principal types of locally convex spaces -- Table II. โ Principal homologies on the dual of a locally convex space -- V. โ Hilbertian spaces (elementary theory) V. -- ยง 1. Prehilbertian spaces and hilbertian spaces -- ยง 2. Orthogonal families in a hilbertian space -- ยง 3. Tensor product of hilbertian spaces -- ยง 4. Some classes of operators in hilbertian spaces -- Exercises on ยง 1 -- Exercises on ยง 2 -- Exercises on ยง 3 -- Exercises on ยง 4 -- Historical notes -- Index of notation -- Index of terminology -- Summary of some important properties of Banach spaces