《NORMED LINEAR SPACES》

Chapter Ⅰ．Linear spaces1

1．Linear spaces and linear dependence1

2．Linear functions and conjugate spaces4

3．The Hahn-Banach extension theorem8

4．Linear topological spaces11

5．Conjugate spaces17

6．Cones，wedges，order relations20

Chapter Ⅱ．Normed Linear spaces24

1．Elementary definitions and properties24

2．Examples of normed spaces；constructions of new spaces from old28

3．Category proofs33

4．Geometry and approximation38

5．Comparison of topologies in a normed space39

Chapter Ⅲ．Completeness，compactness，and reflexivity44

1．Completeness in a linear topological space44

2．Compactness47

3．Completely continuous linear operators53

4．Reflexivity56

Chapter Ⅳ．Unconditional convergence and bases58

1．Series and unconditional convergence58

2．Tensor products of locally convex spaces63

3．Schauder bases in separable spaces67

4．Unconditional bases73

Chapter Ⅴ．Compact convex sets and continuous function spaces77

1．Extreme points of compact convex sets77

2．The fixed-point theorem82

3．Some properties of continuous function spaces84

4．Characterizations of continuous function spaces among Banach spaces87

Chapter Ⅵ．Norm and order96

1．Vector lattices and normed lattices96

2．Linear sublattices of continuous function spaces101

3．Monotone projections and extensions104

4．Special properties of(AL)-spaces107

Chapter Ⅶ．Metric geometry in normed spaces110

1．Isometry and the linear structure110

2．Rotundity and smoothness111

3．Characterizations of inner-product spaces115

Chapter Ⅷ．Reader＇s guide121

Bibliography124

Index of symbols132

Index135