Topological Vector Spaces

Start reading → Topological vector spaces over a valued division ring

1. Front matter
   1. To the reader
2. ITopological vector spaces over a valued division ring
   1. Topological vector spaces over a valued division ring
   2. § 1. Topological vector spaces27
   3. § 2. Linear varieties in a topological vector space26
   4. § 3. Metrisable topological vector spaces11
3. IIConvex sets and locally convex spaces
   1. Convex sets and locally convex spaces
   2. § 1. Semi-norms15
   3. § 2. Convex sets51
   4. § 3. The Hahn-Banach Theorem (analytic form)6
   5. § 4. Locally convex spaces33
   6. § 5. Separation of convex sets24
   7. § 6. Weak topologies41
   8. § 7. Extremal points and extremal generators25
   9. § 8. Complex locally convex spaces10
4. IIISpaces of continuous linear mappings
   1. Spaces of continuous linear mappings
   2. § 1. Bornology in a topological vector space30
   3. § 2. Bornological spaces6
   4. § 3. Spaces of continuous linear mappings39
   5. § 4. The Banach-Steinhaus theorem24
   6. § 5. Hypocontinuous bilinear mappings16
   7. § 6. Borel's graph theorem8
5. IVDuality in topological vector spaces
   1. Duality in topological vector spaces
   2. § 1. Duality36
   3. § 2. Bidual. Reflexive spaces32
   4. § 3. Dual of a Fréchet space15
   5. § 4. Strict morphisms of Fréchet spaces13
   6. § 5. Compactness criteria8
   7. App. 0. Fixed points of groups of affine transformations10
6. VHilbertian spaces (elementary theory)
   1. Hilbertian spaces (elementary theory)
   2. § 1. Prehilbertian spaces and hilbertian spaces41
   3. § 2. Orthogonal families in a hilbertian space23
   4. § 3. Tensor product of hilbertian spaces20
   5. § 4. Some classes of operators in hilbertian spaces49
   6. Historical Note
7. Indexes
   1. Index of notation
   2. Index of terminology