拓撲向量空間(第二版)

Preface to the Second Edition
Preface
Prerequisites
A. Sets and Order
B. General Topology
C. Linear Algebra
Ⅰ. TOPOLOGICAL VECTOR SPACES Introducction
1 Vector Space Topologies
2 Product Spaces,Subspaces,Direct Sums,Quotient Spaces
3 Topological Vector Spaces of Finite Dimension
4 Linear Manifolds and Hyperplanes
5 Bounded Sets
6 Metrizability
7 Complexification
Exercises
Ⅱ. LOCALLY CONVEX TOPOLOGICAL VECTOR SPACES Introducction
1 Convex Sets and Semi-Norms
2 Normed and Normable Spaces
3 The Hahn-Banach Theorem
4 Locally Convex Spaces
5 Projective Topologies
6 Inductive Topologies
7 Barreled Spaces
8 Bornological Spaces
9 Separation of Convex Sets
10 Compact Convex Sets
Exerises
Ⅲ. LINEAR MAPPINGS Introducction
1 Continuous linear Maps and Topological Homomorphisms
2 Banach’’s Homomorphism Theorem
3 Spaces of Linear Mappings
4 Equicontinuity.The Principle of Uniform Boundedness and the Banach-Steinhaus Theorem
5 Bilinear Mappings
6 Topological Tensor Products
7 Nuclear Mappings and Spaces
8 Examples of Nuclear Spaces
9 The Approximation Property.Compact Maps
Exercises
Ⅳ. DUALITY Introducction
1 Dual Systems and Weak Topologies
2 Elementary Properties of Adjoint Maps
3 Locally Convex Topologies Consistent with a Given Duality.The Mackey-Arens Theorem
4 Duality of Projective and Inductive Topologies
5 Strong Dual of a Localy Convex Space.Bidual.Reflexive Spaces
6 Dual Characterization of Completeness,Metrizable Spaces.Theorems of Grothendieck,Banach-Dieudonne,and Krein-Smulian
……
Ⅴ. ORDER STRUCTURES
Ⅵ. C-AND W-ALGEBRAS
Appendix.SPECTRAL PROPERTIES OF POSITIVE OPERATORS