Title | Vector Lattices and Integral Operators [electronic resource] / edited by S. S. Kutateladze |
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Imprint | Dordrecht : Springer Netherlands, 1996 |
Connect to | http://dx.doi.org/10.1007/978-94-009-0195-7 |
Descript | IX, 462 p. online resource |
1. Nonstandard Theory of Vector Lattices -- 1. Vector Lattices -- 2. Boolean-Valued Models -- 3. Real Numbers in BooleanโValued Models -- 4. Boolean-Valued Analysis of Vector Lattices -- 5. Fragments of Positive Operators -- 6. LatticeโNormed Spaces -- Comments -- References -- 2. Operator Classes Determined by Order Conditions -- 1. Ideal Spaces -- 2. The Space of Regular Operators -- 3. Spaces of Vector-Functions -- 4. Dominated Operators -- Comments -- References -- 3. Stably Dominated and Stably Regular Operators -- 1. pโAbsolutely Summing Operators -- 2. pโAbsolutely Summing Operators in Hilbert Space -- 3. Nuclear Operators -- 4. Stably Dominated Operators -- 5. Coincidence of Some Classes of Operators in the Scale of the Banach Spaces LP -- 6. NikishinโMaurey Factorization Theorems -- 7. Stably Regular Operators -- 8. Certain Operator Lattices -- 9. Operator Spaces and Local Unconditional Structure -- S. Supplement to Chapter 3 -- Comments -- References -- 4. Integral Operators -- 1. Basic Properties of Integral Operators -- 2. Integral Representation of Linear Operators -- 3. Applications of the Criterion for Integral Representability -- 4. Linear Operators and Vector Measures -- 5. Integral Representation of Nonlinear Operators -- 6. Algebraic Properties of Integral Operators -- 7. Universal Integral Operators and Operators with Integral Commutators -- Comments -- References -- S. Supplement to Chapter 4. Integral Operators of Convolution (V.D. Stepanov) -- References -- 5. Disjointness Preserving Operators -- 1. Prerequisites -- 2. Order Approximating Sets -- 3. Order Bounded Operators -- 4. The Shadow of an Operator -- 5. Orthomorphisms -- 6. Shift Operators -- 7. Weighted Shift Operator -- 8. Representation of Disjointness Preserving Operators -- 9. Interpretation for the Properties of Operators -- Comments -- References