Locally Solid Riesz Spaces
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Locally Solid Riesz Spaces With Applications To Economics
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Author : Charalambos D. Aliprantis
language : en
Publisher: American Mathematical Society
Release Date : 2025-05-14
Locally Solid Riesz Spaces With Applications To Economics written by Charalambos D. Aliprantis and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-14 with Mathematics categories.
Riesz space (or a vector lattice) is an ordered vector space that is simultaneously a lattice. A topological Riesz space (also called a locally solid Riesz space) is a Riesz space equipped with a linear topology that has a base consisting of solid sets. Riesz spaces and ordered vector spaces play an important role in analysis and optimization. They also provide the natural framework for any modern theory of integration. This monograph is the revised edition of the authors' book Locally Solid Riesz Spaces (1978, Academic Press). It presents an extensive and detailed study (with complete proofs) of topological Riesz spaces. The book starts with a comprehensive exposition of the algebraic and lattice properties of Riesz spaces and the basic properties of order bounded operators between Riesz spaces. Subsequently, it introduces and studies locally solid topologies on Riesz spaces— the main link between order and topology used in this monograph. Special attention is paid to several continuity properties relating the order and topological structures of Riesz spaces, the most important of which are the Lebesgue and Fatou properties. A new chapter presents some surprising applications of topological Riesz spaces to economics. In particular, it demonstrates that the existence of economic equilibria and the supportability of optimal allocations by prices in the classical economic models can be proven easily using techniques from the theory of topological Riesz spaces. At the end of each chapter there are exercises that complement and supplement the material in the chapter. The last chapter of the book presents complete solutions to all exercises. Prerequisites are the fundamentals of real analysis, measure theory, and functional analysis. This monograph will be useful to researchers and graduate students in mathematics. It will also be an important reference tool to mathematical economists and to all scientists and engineers who use order structures in their research.
Locally Solid Riesz Spaces
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Author : Charalambos D. Aliprantis
language : en
Publisher:
Release Date : 1978
Locally Solid Riesz Spaces written by Charalambos D. Aliprantis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
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.
Locally Solid Riesz Spaces With Applications To Economics
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Author : Charalambos D. Aliprantis
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Locally Solid Riesz Spaces With Applications To Economics written by Charalambos D. Aliprantis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Business & Economics categories.
Riesz space (or a vector lattice) is an ordered vector space that is simultaneously a lattice. A topological Riesz space (also called a locally solid Riesz space) is a Riesz space equipped with a linear topology that has a base consisting of solid sets. Riesz spaces and ordered vector spaces play an important role in analysis and optimization. They also provide the natural framework for any modern theory of integration. This monograph is the revised edition of the authors' bookLocally Solid Riesz Spaces (1978, Academic Press). It presents an extensive and detailed study (with complete proofs) of topological Riesz spaces. The book starts with a comprehensive exposition of the algebraic and lattice properties of Riesz spaces and the basic properties of order bounded operatorsbetween Riesz spaces. Subsequently, it introduces and studies locally solid topologies on Riesz spaces-- the main link between order and topology used in this monograph. Special attention is paid to several continuity properties relating the order and topological structures of Riesz spaces, the most important of which are the Lebesgue and Fatou properties. A new chapter presents some surprising applications of topological Riesz spaces to economics. In particular, it demonstrates that theexistence of economic equilibria and the supportability of optimal allocations by prices in the classical economic models can be proven easily using techniques At the end of each chapter there are exercises that complement and supplement the material in the chapter. The last chapter of the book presentscomplete solutions to all exercises. Prerequisites are the fundamentals of real analysis, measure theory, and functional analysis. This monograph will be useful to researchers and graduate students in mathematics. It will also be an important reference tool to mathematical economists and to all scientists and engineers who use order structures in their research.
Locally Solid Riesz Spaces With Applications To Economics
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Author : Charalambos D. Aliprantis
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-05-21
Locally Solid Riesz Spaces With Applications To Economics written by Charalambos D. Aliprantis and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-21 with MATHEMATICS categories.
Riesz space (or a vector lattice) is an ordered vector space that is simultaneously a lattice. A topological Riesz space (also called a locally solid Riesz space) is a Riesz space equipped with a linear topology that has a base consisting of solid sets. Riesz spaces and ordered vector spaces play an important role in analysis and optimization. They also provide the natural framework for any modern theory of integration. This monograph is the revised edition of the authors' book Locally Solid Riesz Spaces (1978, Academic Press). It presents an extensive and detailed study (with complete proofs) of topological Riesz spaces. The book starts with a comprehensive exposition of the algebraic and lattice properties of Riesz spaces and the basic properties of order bounded operators between Riesz spaces. Subsequently, it introduces and studies locally solid topologies on Riesz spaces-- the main link between order and topology used in this monograph. Special attention is paid to several continuity properties relating the order and topological structures of Riesz spaces, the most important of which are the Lebesgue and Fatou properties. spaces to economics. In particular, it demonstrates that the existence of economic equilibria and the supportability of optimal allocations by prices in the classical economic models can be proven easily using techniques At the end of each chapter there are exercises that complement and supplement the material in the chapter. The last chapter of the book presents complete solutions to all exercises. Prerequisites are the fundamentals of real analysis, measure theory, and functional analysis. This monograph will be useful to researchers and graduate students in mathematics. It will also be an important reference tool to mathematical economists and to all scientists and engineers who use order structures in their research.
Infinite Dimensional Analysis
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Author : Charalambos D. Aliprantis
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-02
Infinite Dimensional Analysis written by Charalambos D. Aliprantis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-02 with Business & Economics categories.
This monograph presents a study of modern functional analysis. It is intended for the student or researcher who could benefit from functional analytic methods, but does not have an extensive background and does not plan to make a career as a functional analyst.
Topological Riesz Spaces And Measure Theory
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Author : D. H. Fremlin
language : en
Publisher: Cambridge University Press
Release Date : 1974-02-28
Topological Riesz Spaces And Measure Theory written by D. H. Fremlin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-02-28 with Mathematics categories.
Dr Fremlin's aim in writing this book is to identify those concepts in measure theory which are most relevant to functional analysis and to integrate them into functional analysis in a way consistent with that subject's structure and habits of thought. This is achieved by approaching measure theory through the properties of Riesz spaces and especially topological Riesz spaces.
Existence And Optimality Of Competitive Equilibria
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Author : Charalambos D. Aliprantis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Existence And Optimality Of Competitive Equilibria written by Charalambos D. Aliprantis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Business & Economics categories.
This monograph is a systematic exposition of the authors' research on general equi librium models with an infinite number of commodities. It is intended to serve both as a graduate text on aspects of general equilibrium theory and as an introduction, for economists and mathematicians working in mathematical economics, to current research in a frontier area of general equilibrium theory. To this end, we have pro vided two introductory chapters on the basic economic model and the mathematical framework. The exercises at the end of each section complement the main exposition. Chapter one is a concise but substantiative discussion of the questions of exis tence and optimality of competitive equilibria in the Walrasian general equilibrium model of an economy with a finite number of households, firms and commodities. Our extension of this model to economies with an infinite number of commodities constitutes the core material of this book and begins in chapter three. Readers fa miliar with the Walrasian general equilibrium model as exposited in (13], [23] or [52] may treat chapter one as a handy reference for the main economic concepts and notions that are used throughout the book.
Locally Solid Riesz Spaces
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Author : Charalambos D. Aliprantis
language : it
Publisher:
Release Date : 1978
Locally Solid Riesz Spaces written by Charalambos D. Aliprantis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with categories.
Positive Operators
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Author : Charalambos D. Aliprantis
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-10-21
Positive Operators written by Charalambos D. Aliprantis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-21 with Computers categories.
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.
Canadian Journal Of Mathematics
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Author :
language : en
Publisher:
Release Date : 1980-06
Canadian Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-06 with categories.