Banach Lattices and Operators

Title Page......Page 1
Copyright Information......Page 2
Preface......Page 4
Contents......Page 6
0. Notations and preliminaries......Page 8
1. Ordered vector spaces......Page 11
2. Vector lattices......Page 16
3. Sublattices, ideals, bands......Page 26
4. Order completeness and projection properties......Page 34
5. Linear operators and functionals......Page 45
6. Order continuous functionals......Page 55
7. Ideal function spaces......Page 61
1. Normed lattices......Page 66
2. Linear operators and functionals......Page 70
3. Banach lattices with order continuous norm......Page 76
4. Banach lattices with the Fatou property......Page 82
5. Monotonically complete Banach lattices......Page 85
6. KB-spaces......Page 87
7. Reflexive Banach lattices......Page 92
8. Separable Banach lattices......Page 97
9. AM- and AL-spaces......Page 99
10. AM-spaces, order properties......Page 113
11. AL_p -spaces......Page 121
12. Homogeneous functions on a Banach lattice......Page 123
13. Banach function spaces......Page 128
1. Moduli of operators......Page 136
2. Regular operators......Page 139
3. Finite operators......Page 147
4. Operator modules......Page 154
5. Adjoint operator modules......Page 162
6. (p,q)-convex and (p,q)-concave operators......Page 173
7. p-superadditive and p-subadditive operators......Page 180
8. Operator characterizations of Banach lattices......Page 188
Bibliography......Page 202
Index......Page 207
List of symbols......Page 209