Locally Solid Riesz Spaces With Applications To Economics
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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(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.
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.
Pre Riesz Spaces
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Author : Anke Kalauch
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-11-19
Pre Riesz Spaces written by Anke Kalauch and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-19 with Mathematics categories.
This monograph develops the theory of pre-Riesz spaces, which are the partially ordered vector spaces that embed order densely into Riesz spaces. Concepts from Riesz space theory such as disjointness, ideals, and bands are extended to pre-Riesz spaces. The analysis revolves around embedding techniques, including the Riesz completion and the functional representation. In the same spirit, norms and topologies on a pre-Riesz space and their extensions to the Riesz completion are examined. The generalized concepts are used to investigate disjointness preserving operators on pre-Riesz spaces and related notions. The monograph presents recent results as well as being an accessible introduction to the theory of partially ordered vector spaces and positive operators. Contents A primer on ordered vector spaces Embeddings, covers, and completions Seminorms on pre-Riesz spaces Disjointness, bands, and ideals in pre-Riesz spaces Operators on pre-Riesz spaces
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.
Positivity And Noncommutative Analysis
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Author : Gerard Buskes
language : en
Publisher: Springer
Release Date : 2019-08-09
Positivity And Noncommutative Analysis written by Gerard Buskes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-09 with Mathematics categories.
Capturing the state of the art of the interplay between positivity, noncommutative analysis, and related areas including partial differential equations, harmonic analysis, and operator theory, this volume was initiated on the occasion of the Delft conference in honour of Ben de Pagter's 65th birthday. It will be of interest to researchers in positivity, noncommutative analysis, and related fields. Contributions by Shavkat Ayupov, Amine Ben Amor, Karim Boulabiar, Qingying Bu, Gerard Buskes, Martijn Caspers, Jurie Conradie, Garth Dales, Marcel de Jeu, Peter Dodds, Theresa Dodds, Julio Flores, Jochen Glück, Jacobus Grobler, Wolter Groenevelt, Markus Haase, Klaas Pieter Hart, Francisco Hernández, Jamel Jaber, Rien Kaashoek, Turabay Kalandarov, Anke Kalauch, Arkady Kitover, Erik Koelink, Karimbergen Kudaybergenov, Louis Labuschagne, Yongjin Li, Nick Lindemulder, Emiel Lorist, Qi Lü, Miek Messerschmidt, Susumu Okada, Mehmet Orhon, Denis Potapov, Werner Ricker, Stephan Roberts, Pablo Román, Anton Schep, Claud Steyn, Fedor Sukochev, James Sweeney, Guido Sweers, Pedro Tradacete, Jan Harm van der Walt, Onno van Gaans, Jan van Neerven, Arnoud van Rooij, Freek van Schagen, Dominic Vella, Mark Veraar, Anthony Wickstead, Marten Wortel, Ivan Yaroslavtsev, and Dmitriy Zanin.
Topological Vector Spaces And Their Applications
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Author : V.I. Bogachev
language : en
Publisher: Springer
Release Date : 2017-05-16
Topological Vector Spaces And Their Applications written by V.I. Bogachev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-16 with Mathematics categories.
This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. Overall, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.
Mathematical Analysis And Applications In Modeling
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Author : Priti Kumar Roy
language : en
Publisher: Springer Nature
Release Date : 2020-03-10
Mathematical Analysis And Applications In Modeling written by Priti Kumar Roy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-10 with Mathematics categories.
This book collects select papers presented at the “International Conference on Mathematical Analysis and Application in Modeling,” held at Jadavpur University, Kolkata, India, on 9–12 January 2018. It discusses new results in cutting-edge areas of several branches of mathematics and applications, including analysis, topology, dynamical systems (nonlinear, topological), mathematical modeling, optimization and mathematical biology. The conference has emerged as a powerful forum, bringing together leading academics, industry experts and researchers, and offering them a venue to discuss, interact and collaborate in order to stimulate the advancement of mathematics and its industrial applications.
Modeling Foundations Of Economic Property Rights Theory
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Author : Vesna Pasetta
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Modeling Foundations Of Economic Property Rights Theory written by Vesna Pasetta 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 2006-03-30 with Business & Economics categories.
This is an introduction to the foundations of economic property rights t- ory (EPRT). In this volume, a ?rst step in the EPRT research program, rules concerningeconomicpropertyrights(e. p. r. s),entrepreneurialagreements,and enterprises are discussed. Introduced concept of e. p. r. s is an extension of the traditional concept of pairing of residual rights of control and residual rights of returns in the economic theory. Its importance in economics is generated fromageneralimpossibilityofmakingacompletecontract,concerninge. p. r. s, for any nontrivial economic transaction. The volume o?ers a theoretical - tension of mathematical economics, applying recent results of Hopf algebras, quasi-Hopf algebras, representation theory, theory of categories, and defor- tion theories, in looking for suitable mathematical methodology of economic property rights theories and foundations of general theory of economic agr- ments. The idea is to construct a kind of mathematical application in which any fundamental formal entity and/or operation has an empirical economic interpretation. This approach is seen as a way to cope with an extreme c- plexity of economic phenomena under consideration and requests for precise formulationofmodelswheremeaningfulanswersandsolutionsofproblemsare only those which are obtained rigorously. The proposed extensions in ma- ematical economics and property rights theory are to provide rich enough foundations to follow complexity of economic property rights in the exact way, and to identify where there is an appropriate method providing a- quate solution, and also to ?nd problems where in general there is no such methodology.
Financial Economics
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Author : Thorsten Hens
language : en
Publisher: Springer
Release Date : 2016-06-01
Financial Economics written by Thorsten Hens and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-01 with Business & Economics categories.
Financial economics is a fascinating topic where ideas from economics, mathematics and, most recently, psychology are combined to understand financial markets. This book gives a concise introduction into this field and includes for the first time recent results from behavioral finance that help to understand many puzzles in traditional finance. The book is tailor made for master and PhD students and includes tests and exercises that enable the students to keep track of their progress. Parts of the book can also be used on a bachelor level. Researchers will find it particularly useful as a source for recent results in behavioral finance and decision theory.
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.