Foreword ........................................................ 9
Chapter 0
Preliminaries .................................................. 11
0.1. Basic properties of vector lattices .................... 11
0.2. Special subspaces of vector lattices and some types
of vector lattices ..................................... 15
0.3. Order bounded operators ................................ 19
0.4. Normed and Banach lattices ............................. 25
0.5. Classical sequence Banach lattices ..................... 33
0.6. Locally solid vector lattices .......................... 40
Chapter 1
The notion of order continuity and its characterizations by
order properties ............................................... 43
Chapter 2
Characterizations of order continuity by properties of
functionals .................................................... 66
Chapter 3
Order type characterizations of dual Banach lattices with
order continuous norms ......................................... 70
Chapter 4
Order continuity as a topological invariant .................... 73
Chapter 5
Operator characterizations of order continuity ................. 83
Chapter 6
Discrete and continuous Banach lattices with order
continuous norms ............................................... 91
Chapter 7
KB-spaces ..................................................... 101
Chapter 8
Reflexive Banach lattices ..................................... 112
Remarks on other characterizations ............................ 117
References .................................................... 119
List of symbols ............................................... 124
Index ......................................................... 126
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