Cones and DualityAmerican Mathematical Soc., 12.06.2007 - 279 Seiten Ordered vector spaces and cones made their debut in mathematics at the beginning of the twentieth century. They were developed in parallel (but from a different perspective) with functional analysis and operator theory. Before the 1950s, ordered vector spaces appeared in the literature in a fragmented way. Their systematic study began around the world after 1950 mainly through the efforts of the Russian, Japanese, German, and Dutch schools. Since cones are being employed to solve optimization problems, the theory of ordered vector spaces is an indispensable tool for solving a variety of applied problems appearing in several diverse areas, such as engineering, econometrics, and the social sciences. For this reason this theory plays a prominent role not only in functional analysis but also in a wide range of applications. This is a book about a modern perspective on cones and ordered vector spaces. It includes material that has not been presented earlier in a monograph or a textbook. With many exercises of varying degrees of difficulty, the book is suitable for graduate courses. Most of the new topics currently discussed in the book have their origins in problems from economics and finance. Therefore, the book will be valuable to any researcher and graduate student who works in mathematics, engineering, economics, finance, and any other field that uses optimization techniques. |
Inhalt
Cones | 1 |
Cones in topological vector spaces | 61 |
Yudin and pullback cones | 117 |
Krein operators | 159 |
Klattices | 173 |
The order extension of L | 197 |
Piecewise affine functions | 221 |
linear topologies | 243 |
Bibliography | 265 |
Index | 271 |
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Häufige Begriffe und Wortgruppen
affine functions assume Banach space closed cone cone L+ contradiction convex set Corollary Dedekind complete defined denote dimensional vector space Exercise exists extremal rays extremal vectors extreme point finite finite dimensional vector first fix function f G L+ Hint holds true ice cream cone implies Int(Si interior point isomorphism K-lattice K-strictly Krein operator Krein space lattice cone Lb(L Lemma linear topology locally convex space locally convex topology nonempty subset normal cone normed space order bounded order intervals order unit ordered Banach space ordered topological vector ordered vector space piecewise affine functions pointwise polyhedral wedge polyhedron polytope positive linear functional positive operator positive vectors positively homogeneous Proof result Riesz decomposition property Riesz space Riesz subspace RieszIKantorovich satisfies satisfying scalar seminorms sequence Show superadditive supremum Theorem topological vector space vector lattice vector ordering vector subspace weakly compact zero