Download or read book Positive Operators Riesz Spaces and Economics written by Charalambos D. Aliprantis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last fifty years advanced mathematical tools have become an integral part in the development of modern economic theory. Economists continue to invoke sophisticated mathematical techniques and ideas in order to understand complex economic and social problems. In the last ten years the theory of Riesz spaces (vector lattices) has been successfully applied to economic theory. By now it is understood relatively well that the lattice structure of Riesz spaces can be employed to capture and interpret several economic notions. On April 16-20, 1990, a small conference on Riesz Spaces, Positive Opera tors, and their Applications to Economics took place at the California Institute of Technology. The purpose of the conference was to bring mathematicians special ized in Riesz Spaces and economists specialized in General Equilibrium together to exchange ideas and advance the interdisciplinary cooperation between math ematicians and economists. This volume is a collection of papers that represent the talks and discussions of the participants at the week-long conference. We take this opportunity to thank all the participants of the conference, especially those whose articles are contained in this volume. We also greatly ap preciate the financial support provided by the California Institute of Technology. In particular, we express our sincerest thanks to David Grether, John Ledyard, and David Wales for their support. Finally, we would like to thank Susan Davis, Victoria Mason, and Marge D'Elia who handled the delicate logistics for the smooth running of the confer ence.
Download or read book Positive Operators Riesz Spaces and Economics written by Charalambos D. Aliprantis and published by . This book was released on 2011-05-08 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Positive Operators Riesz Spaces and Economics written by Charalambos D. Aliprantis and published by . This book was released on 1991 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Locally Solid Riesz Spaces with Applications to Economics written by Charalambos D. Aliprantis and published by American Mathematical Soc.. This book was released on 2003 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Functional Analysis and Economic Theory written by Yuri Abramovich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: In July of 1996, the conference Nonlinear Analysis and its Applications in Engineering and Economics took place on the Greek island of Samos, the birthplace of Pythagoras. During this conference, a special session was held on th the occasion of the 50 birthday of the well known mathematician and math ematical economist Professor Charalambos Aliprantis, who, by his numerous friends, is usually called Roko. The story behind this nickname is not quite clear yet; it will be investigated further and will be made public prior to his th 60 birthday. (At this moment we have already found out that it has nothing to do with the famous movie Rocco and his Brothers even though Roko does have two brothers. ) Roko was born on the Greek island of Cephalonia on May 12,1946, and his elementary and secondary school education took place there. At 18 he entered the Mathematics Department at the University of Athens. Upon graduation from the University of Athens he proceeded with his graduate studies at Cal tech, where in 1973 he completed his Ph. D. degree in Mathematics under the supervision of Professor W. A. J. Luxemburg. His research career can be divided into two periods. The first one, till 1981, was devoted entirely to pure mathematics. The other one, after 1981, has been subdivided between pure mathematics and mathematical economics. The main objects of Roko's work in pure mathematics are spaces with order structure (Riesz spaces) and operators acting on them.
Download or read book Positive Operators written by Charalambos D. Aliprantis and published by Springer Science & Business Media. This book was released on 2006-10-21 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reprinted by popular demand, this monograph presents a comprehensive study of positive operators between Riesz spaces and Banach lattices. Since publication of this book in 1985, the subject of positive operators and Riesz spaces has found practical applications in disciplines including social sciences and engineering. This book examines positive operators in the setting of Riesz spaces and Banach lattices, from both the algebraic and topological points of view.
Download or read book Finite Elements in Vector Lattices written by Martin R. Weber and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-08-20 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is the first systematical treatment of the theory of finite elements in Archimedean vector lattices and contains the results known on this topic up to the year 2013. It joins all important contributions achieved by a series of mathematicians that can only be found in scattered in literature.
Download or read book Infinite Dimensional Analysis written by Charalambos D. Aliprantis and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text was born out of an advanced mathematical economics seminar at Caltech in 1989-90. We realized that the typical graduate student in mathematical economics has to be familiar with a vast amount of material that spans several traditional fields in mathematics. Much of the mate rial appears only in esoteric research monographs that are designed for specialists, not for the sort of generalist that our students need be. We hope that in a small way this text will make the material here accessible to a much broader audience. While our motivation is to present and orga nize the analytical foundations underlying modern economics and finance, this is a book of mathematics, not of economics. We mention applications to economics but present very few of them. They are there to convince economists that the material has so me relevance and to let mathematicians know that there are areas of application for these results. We feel that this text could be used for a course in analysis that would benefit math ematicians, engineers, and scientists. Most of the material we present is available elsewhere, but is scattered throughout a variety of sources and occasionally buried in obscurity. Some of our results are original (or more likely, independent rediscoveries). We have included some material that we cannot honestly say is neces sary to understand modern economic theory, but may yet prove useful in future research.
Download or read book Cones and Duality written by Charalambos D. Aliprantis and published by American Mathematical Soc.. This book was released on 2007-06-12 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordered vector spaces and cones made their debut in mathematics at the beginning of the twentieth century. They were developed in parallel (but from a different perspective) with functional analysis and operator theory. Before the 1950s, ordered vector spaces appeared in the literature in a fragmented way. Their systematic study began around the world after 1950 mainly through the efforts of the Russian, Japanese, German, and Dutch schools. Since cones are being employed to solve optimization problems, the theory of ordered vector spaces is an indispensable tool for solving a variety of applied problems appearing in several diverse areas, such as engineering, econometrics, and the social sciences. For this reason this theory plays a prominent role not only in functional analysis but also in a wide range of applications. This is a book about a modern perspective on cones and ordered vector spaces. It includes material that has not been presented earlier in a monograph or a textbook. With many exercises of varying degrees of difficulty, the book is suitable for graduate courses. Most of the new topics currently discussed in the book have their origins in problems from economics and finance. Therefore, the book will be valuable to any researcher and graduate student who works in mathematics, engineering, economics, finance, and any other field that uses optimization techniques.
Download or read book Pre Riesz Spaces written by Anke Kalauch and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-19 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Problems in Equilibrium Theory written by Charalambos D. Aliprantis and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to teach the basic methods of proof and problem solving in General Equilibrium Theory at graduate level. The problems cover the entire spectrum of difficulty: some are routine, while others require a good grasp of the material involved, and some are even challenging. In searching for the basic required techniques, students will discover a wealth of new material, and are encouraged to arrive at solutions different from the ones presented in the book. Complete solutions to two hundred problems are provided.
Download or read book Handbook of Mathematics written by I.N. Bronshtein and published by Springer. This book was released on 2015-03-19 with total page 1255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emphasis was laid on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing. Besides many enhancements and new paragraphs, new sections on Geometric and Coordinate Transformations, Quaternions and Applications, and Lie Groups and Lie Algebras were added for the sixth edition.
Download or read book Equilibrium Theory in Infinite Dimensional Spaces written by M. Ali Khan and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: Apart from the underlying theme that all the contributions to this volume pertain to models set in an infinite dimensional space, they differ on many counts. Some were written in the early seventies while others are reports of ongoing research done especially with this volume in mind. Some are surveys of material that can, at least at this point in time, be deemed to have attained a satisfactory solution of the problem, while oth ers represent initial forays into an original and novel formulation. Some furnish alternative proofs of known, and by now, classical results, while others can be seen as groping towards and exploring formulations that have not yet reached a definitive form. The subject matter also has a wide leeway, ranging from solution concepts for economies to those for games and also including representation of preferences and discussion of purely mathematical problems, all within the rubric of choice variables belonging to an infinite dimensional space, interpreted as a commodity space or as a strategy space. Thus, this is a collective enterprise in a fairly wide sense of the term and one with the diversity of which we have interfered as little as possible. Our motivation for bringing all of this work under one set of covers was severalfold.
Download or read book Decisions Games and Markets written by Pierpaolo Battigalli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Decisions, Games and Markets is designed to stimulate new developments in decision theory, game theory and general equilibrium theory, as well as in their applications to economics. The book is divided into three parts - Decision Theory, Game Theory, and the Theory of Markets. Though its orientation is primarily methodological, some articles are more applied. The consistent use of formal analysis and methodological individualism constitutes the unifying theme of the book. Decisions, Games and Markets will be of considerable interest to both students and teachers of microeconomics and game and decision theory.
Download or read book Current Topics in Quantitative Finance written by Elio Canestrelli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume collects a selection of revised papers which were presented at the 21st Euro Working Group on Financial Modelling Meeting, held in Venice (Italy), on October 29-31, 1997. The Working Group was founded in September 1986 in Lisbon with the objective of providing an international forum for the exchange of information and experience; encouraging research and interaction be tween financial economic theory and practice of financial decision mak ing, as well as circulating information among universities and financial institutions throughout Europe. The attendance to the Meeting was large and highly qualified. More than 80 participants, coming from 20 different Countries debated on 5 invited lectures and 40 communications in regular sessions. The sessions were located at the Island of San Servolo, on the Venetian lagoon, just in front of the Doges Palace. San Servolo Island is a natural oasis, in the midst of a unique urban setting, offering great relaxation in a peaceful park and a panoramic view of Venice. The friendly atmosphere added great benefit to the formal and informal discussions among the participants, -which is typical of E.W.G.F.M. Meetings. It is interesting to consider the story of the Meeting. The previous locations were held at Cyprus, Crete and Dubrovnik - former mile stones of the Venitian Republic influence on the Mediterranean Sea. Therefore, that this Meeting should be harboured in the heart of the Republic itself (namely, the Saint Mark basin), was only a matter of consequence.
Download or read book Modeling Foundations of Economic Property Rights Theory written by Vesna Pasetta and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Current Trends in Economics written by Ahmet Alkan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1990, the Society for the Advancement of Economic Theory (SAET) was founded with the main purpose to advance our knowledge in theoretical economics and to facilitate communication among researchers in economics, mathematics, game theory and any other field which is po tentially useful to economic theory. To achieve these goals, SAET sponsors the research journal Economic Theory published by Springer-Verlag and holds international conferences every other year. The first two conferences SAET took place in the island of Cephalonia, Greece, in the summers of of 1993 and 1995. In the summer of 1997, the conference was held in Antalya, Turkey. The twenty-nine papers in this volume are mostly by participants in the Antalya meeting of SAET and form a broad sample of the 150 papers pre sented there. Topics covered include cooperative and noncooperative games, social choice and welfare, bargaining, matchings, auctions, mechanism de sign, general equilibrium, general equilibrium with finance, industrial or ganization, macroeconomics, and experimental economics. We have chosen to present the papers according to the alphabetical order of first author names instead of grouping them by topic or theme. We have appended a complete listing of the sessions in the conference together with a list of program committee members and of sponsors at the end of the volume.
