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This book on Banach space theory focuses on what have been called three-space problems. It contains a fairly complete description of ideas, methods, results and counterexamples. It can be considered self-contained, beyond a course in functional analysis and some familiarity with modern Banach space methods. It will be of interest to researchers for its methods and open problems, and to students for the exposition of techniques and examples.

Functional analysis --- Banach spaces. --- Ultraproducts. --- Duality theory (Mathematics) --- Banach spaces --- Ultraproducts --- Calculus --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Banach [Espaces de ] --- Banach [Ruimten van ] --- Dualiteit [Theorie van de ] (Wiskunde) --- Dualité [Théorie de la ] (Mathématiques) --- Mathematics duality theory --- Theorie van de dualiteit (Wiskunde) --- Théorie de la dualité (Mathématiques) --- Functional analysis. --- Topology. --- Geometry. --- Functional Analysis. --- Euclid's Elements --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations

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Dual arguments have become a standard tool for analysis of problems involving optimization by consumers and producers. The principal aim of this book is to provide a fairly systematic yet simple exposition of the basic structure of such arguments. The emphasis is not on providing mathematically general proofs; instead, a geometric approach is used to provide, in an informal way, an intuitive understanding of duality theory. This book introduces the most common alternative ways of representing preferences and technologies, such as indirect utility and distance functions, expenditure and cost functions, and profit and revenue functions. and it discusses the assumptions under which alternative formulations contain precisely the same information. Results such as Roy's identity. the Hotelling-Wold identity, and Shephard's lemma are fully explained. as are their roles in facilitating analysis of behaviour.

330.1 --- 330.1 Economische grondbegrippen. Algemene begrippen in de economie --- Economische grondbegrippen. Algemene begrippen in de economie --- Analyse microéconomique --- Courbe de demande (Theorie economique) --- Demand functions (Economic theory) --- Dualiteit [Theorie van de ] (Wiskunde) --- Dualité [Théorie de la ] (Mathématiques) --- Mathematics duality theory --- Theorie van de dualiteit (Wiskunde) --- Théorie de la dualité (Mathématiques) --- Verbruikers --- Vraagcurve (Economische theorie) --- DEMAND FUNCTIONS (Economic theory) --- Consumer behavior --- Duality theory (Mathematics) --- Econometric models --- Microeconomics --- Price theory --- Economics --- Econometrics --- Mathematical models --- Algebra --- Mathematical analysis --- Topology --- Demand curves (Economic theory) --- Functions, Demand (Economic theory) --- Behavior, Consumer --- Buyer behavior --- Decision making, Consumer --- Human behavior --- Consumer profiling --- Market surveys --- Quantitative methods (economics) --- Econometric models. --- Consumer behavior. --- Microeconomics. --- Consumers --- 330.00 --- 330.3 --- 339.20 --- AA / International- internationaal --- Economische en sociale theorieën: algemeenheden --- Methode in staathuishoudkunde. Statische, dynamische economie. Modellen. Experimental economics --- Verdeling van de goederen en van de inkomens: algemeenheden --- Business, Economy and Management --- Microéconomie --- Modèles économétriques --- Demande (économie politique) --- Dualité, Principe de (mathématiques) --- Consommateurs --- Attitudes --- Microéconomie --- Modèles économétriques --- Demande (économie politique) --- Dualité, Principe de (mathématiques)