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Contents
Chapter 3. Yudin and pull-back cones 117
§3.1. Closed cones in finite dimensional vector spaces 118
§3.2. Directional wedges and Yudin cones 122
§3.3. Polyhedral wedges and cones 131
§3.4. The geometrical structure of polyhedral cones 137
§3.5. Linear inequalities and alternatives 148
§3.6. Pull-back cones of operators 152
Chapter 4. Krein operators 159
§4.1. The concept of a Krein operator 160
§4.2. Eigenvalues of Krein operators 163
§4.3. Fixed points and eigenvectors 167
Chapter 5. K-lattices 173
§5.1. The notion and properties of K-lattices 174
§5.2. The Riesz–Kantorovich transform 183
§5.3. The order extension of £b(L, N) 190
Chapter 6. The order extension of V 197
§6.1. The extension of V 199
§6.2. Generalized Riesz-Kantorovich functionals 204
§6.3. When is the Riesz-Kantorovich functional additive? 210
Chapter 7. Piecewise affine functions 221
§7.1. One-dimensional piecewise affine functions 221
§7.2. Multivariate piecewise affine functions 227
Chapter 8. Appendix: linear topologies 243
§8.1. Linear topologies on vector spaces 244
§8.2. Duality theory 247
§8.3. 6-topologies 249
§8.4. The separation of convex sets 251
§8.5. Normed and Banach spaces 252
§8.6. Finite dimensional topological vector spaces 256
§8.7. The open mapping and the closed graph theorems 257
§8.8. The bounded weak* topology 259
Bibliography 265
Index 271
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