Dominated Operators

Cover
Title page
Foreword to the English Translation
Preface
Chapter 1. Boolean Algebras and Vector Lattices
1.1. Boolean Algebras
1.2. Representation of Boolean Algebras
1.3. Vector Lattices
1.4. Representation of Vector Lattices
1.5. Normed Vector Lattices
1.6. Comments
Chapter 2. Lattice-Normed Spaces
2.1. Preliminaries
2.2. Completion
2.3. Examples
2.4. Continuous Banach Bundles
2.5. Measurable Banach Bundles
2.6. Comments
Chapter 3. Positive Operators
3.1. Operators in Vector Lattices
3.2. Fragments of a Positive Operator
3.3. Orthomorphisms and Lattice Homomorphisms
3.4. Maharam Operators
3.5. Maharam's Extension of Positive Operators
3.6. Comments
Chapter 4. Dominated Operators
4.1. The Space of Dominated Operators
4.2. Decomposability of the Space of Dominated Operators
4.3. Order Continuous Operators
4.4. The Yosida-Hewitt-Type Theorems
4.5. Extension of Dominated Operators
4.6. Comments
Chapter 5. Disjointness Preserving Operators
5.1. Band Preserving Operators
5.2. n-Disjoint Operators
5.3. Weight-Shift-Weight Factorization
5.4. Multiplicative Representation
5.5. Decomposable Operators
5.6. Comments
Chapter 6. Integral Operators
6.1. Vector Integration
6.2. Integral Representation by Quasi-Radon Measures
6.3. Functional Representation of Maharam's Extension
6.4. Integral Operators
6.5. Pseudointegral Operators
6.6. Comments
Chapter 7. Operators in Spaces with Mixed Norm
7.1. Spaces with Mixed Norm
7.2. Summing Operators
7.3. Isometric Classification
7.4. Kaplansky-Hilbert Modules
7.5. AW*-Algebras
7.6. Comments
Chapter 8. Applications of Boolean-Valued Analysis
8.1. Real Numbers in Boolean-Valued Models
8.2. Boolean-Valued Analysis of Vector Lattices
8.3. Boolean-Valued Banach Spaces
8.4. Involutive Banach Algebras
8.5. Cyclically Compact Operators
8.6. Comments
Appendix. Boolean-Valued Models
References
Symbol Index
Subject Index