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Operator theory --- Banach lattices --- Categories (Mathematics) --- Linear operators --- Positive operators --- Operators, Positive --- Linear maps --- Maps, Linear --- Operators, Linear --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Lattices, Banach --- Banach algebras --- Lattice theory --- Linear operators. --- Lattice theory. --- Catégories (mathématiques) --- Treillis, Théorie des. --- Opérateurs linéaires.

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Reprinted by popular demand, this monograph presents a comprehensive study of positive operators between Riesz spaces and Banach lattices. Since the first publication of this book, (Academic Press, 1985), the subject of positive operators and Riesz spaces has found many applications in several disciplines, including social sciences and engineering. It is well known that many linear operators between Banach spaces arising in classical analysis are in fact positive operators. Therefore we study here positive operators in the setting of Riesz spaces and Banach lattices and from both the algebraic and topological points of view. Special emphasis is given to the compactness properties of positive operators and their relations to the order structures of the spaces the operators are acting upon. In order to make the book as self-sufficient as possible, some basic results from the theory of Riesz spaces and Banach lattices are included with proofs where necessary. However, familiarity with the elementary concepts of real analysis and functional analysis is assumed. The book is divided into five chapters, each consisting of nineteen sections all ending with exercises designed to supplement and illustrate the material.

Positive operators. --- Operators, Positive --- Linear operators --- Computer science. --- Global analysis (Mathematics). --- Mathematics. --- Mathematics of Computing. --- Analysis. --- Applications of Mathematics. --- Game Theory, Economics, Social and Behav. Sciences. --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Informatics --- Computer science—Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Game theory. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Engineering --- Engineering analysis --- Mathematical analysis --- 517.1 Mathematical analysis

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This book contains nine well-organized survey articles by leading researchers in positivity, with a strong emphasis on functional analysis. It provides insight into the structure of classical spaces of continuous functions, f-algebras, and integral operators, but also contains contributions to modern topics like vector measures, operator spaces, ordered tensor products, non-commutative Banach function spaces, and frames. Contributors: B. Banerjee, D.P. Blecher, K. Boulabiar, Q. Bu, G. Buskes, G.P. Curbera, M. Henriksen, A.G. Kusraev, J. Mart??-nez, B. de Pagter, W.J. Ricker, A.R. Schep, A. Tri

Ordered algebraic structures. --- Vector valued functions. --- Functional analysis. --- Positive operators. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Algebra --- Operators, Positive --- Linear operators --- Functions, Vector --- Functions, Vector valued --- Functional analysis --- Functions of real variables --- Global analysis (Mathematics). --- Algebra. --- Operator theory. --- Cell aggregation --- Economics. --- Analysis. --- Order, Lattices, Ordered Algebraic Structures. --- Functional Analysis. --- Operator Theory. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Economics, general. --- Mathematics. --- Economic theory --- Political economy --- Social sciences --- Economic man --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Mathematics --- Mathematical analysis --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis. --- Analysis (Mathematics). --- Manifolds (Mathematics). --- Complex manifolds. --- Management science. --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- 517.1 Mathematical analysis