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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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Functional analysis --- Espaces vectoriels topologiques ordonnés. --- Linear topological spaces, Ordered --- Riesz spaces --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Mathematical Theory --- Riesz vector spaces --- Vector lattices --- Lattice theory --- Vector spaces --- Riesz spaces. --- Espaces vectoriels topologiques ordonnés.

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Mathematical analysis --- Functions of real variables --- Functions of real variables. --- Mathematical analysis.

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Mathematical analysis --- Operational research. Game theory --- Mathematics --- Computer science --- Computer. Automation --- analyse (wiskunde) --- toegepaste wiskunde --- informatica --- speltheorie --- wiskunde

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Riesz spaces are named after Frigyes Riesz who first defined them in his 1928 paper "Sur la décomposition des opérations fonctionelles linéaires." Most early work on Riesz spaces addressed the algebraic side of the theory, ignoring the analytic implications, but exploring normed Riesz spaces and Banach lattices. This book concentrates on the general theory of topological Riesz spaces, with a unified approach to locally solid Riesz spaces, emphasizing the relationship between the order structure and the topological structure.

Functional analysis