A course on topological vector spaces

Preface......Page 6
Contents......Page 8
1 Initial Topology, Topological Vector Spaces, Weak Topology......Page 10
2 Convexity, Separation Theorems, Locally Convex Spaces......Page 19
3 Polars, Bipolar Theorem, Polar Topologies......Page 30
4 The Tikhonov and Alaoglu–Bourbaki Theorems......Page 36
5 The Mackey–Arens Theorem......Page 43
6 Topologies on E\'\', Quasi-barrelled and Barrelled Spaces......Page 50
7 Fréchet Spaces and DF-Spaces......Page 58
8 Reflexivity......Page 68
9 Completeness......Page 75
10 Locally Convex Final Topology, Topology of D(Ω)......Page 84
11 Precompact – Compact – Complete......Page 95
12 The Banach–Dieudonné and Krein–Šmulian Theorems......Page 98
13 The Eberlein–Šmulian and Eberlein–Grothendieck Theorems......Page 104
14 Krein\'s Theorem......Page 113
15 Weakly Compact Sets in L1(μ)......Page 118
16 B0=B......Page 124
17 The Krein–Milman Theorem......Page 130
A The Hahn–Banach Theorem......Page 138
B Baire\'s Theorem and the Uniform Boundedness Theorem......Page 142
References......Page 145
Index of Notation......Page 148
Index......Page 150