Background
Aliprantis, Charalambos Dionisios was born on May 12, 1946 in Cephalonia, Greece. Came to United States, 1969. Son of Dionisios Elias and Sofronia Aliprantis.
(The volume contains the proceedings of a conference in ma...)
The volume contains the proceedings of a conference in mathematical economics held at the California Institute of Technology, April 16-20, 1990. The theme of the conference was to explore the functional analytic techniques (and in particular the theory of Riesz spaces and positive operators) that are employed in economics. The articles in the book depict this important connection and open the way for more economic applications.
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(An Invitation to Operator Theory offers a comprehensive a...)
An Invitation to Operator Theory offers a comprehensive and reader-friendly exposition of the theory of linear operators on Banach spaces and Banach. Abramovich and Aliprantis give a unique presentation that includes many new developments in operator theory and also draws together results that are spread over the vast literature. For instance, invariant subspaces of positive operators and the Daugavet equation are presented in monograph form for the first time. The authors keep the discussion self-contained and use exercises to achieve this goal. The book contains over 600 exercises to help students master the material developed in the text. The exercises are of varying degrees of difficulty and play an important and useful role in the exposition. They help to free the proofs of the main results of some technical details but provide students with accurate and complete accounts of how such details ought to be worked out. The exercises also contain a considerable amount of additional material that includes many well-known results whose proofs are not readily available elsewhere. The companion volume, Problems in Operator Theory, also by Abramovich and Aliprantis, is available from the AMS as Volume 51 in the Graduate Studies in Mathematics series, and it contains complete solutions to all exercises in An Invitation to Operator Theory. The solutions demonstrate explicitly technical details in the proofs of many results in operator theory, providing the reader with rigorous and complete accounts of such details. Finally, the book offers a considerable amount of additional material and further developments. By adding extra material to many exercises, the authors have managed to keep the presentation as self-contained as possible. The best way of learning mathematics is by doing mathematics, and the book Problems in Operator Theory will help achieve this goal. Prerequisites to each book are the standard introductory graduate courses in real analysis, general topology, measure theory, and functional analysis. An Invitation to Operator Theory is suitable for graduate or advanced courses in operator theory, real analysis, integration theory, measure theory, function theory, and functional analysis. Problems in Operator Theory is a very useful supplementary text in the above areas. Both books will be of great interest to researchers and students in mathematics, as well as in physics, economics, finance, engineering, and other related areas, and will make an indispensable reference tool.
http://www.amazon.com/gp/product/0821833332/?tag=2022091-20
(With the success of its previous editions, Principles of ...)
With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter on Hilbert spaces as well as integrating over 150 new exercises throughout. The new edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the "Daniell Method" and the measure theoretic approach. Students will be challenged by the more than 600 exercises contained in the book. Topics are illustrated by many varied examples, and they provide clear connections between real analysis and functional analysis.
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(Riesz space (or a vector lattice) is an ordered vector sp...)
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.
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(This is the first book to teach the basic methods of proo...)
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.
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(Games and Decision Making, Second Edition, is a unique bl...)
Games and Decision Making, Second Edition, is a unique blend of decision theory and game theory. From classical optimization to modern game theory, authors Charalambos D. Aliprantis and Subir K. Chakrabarti show the importance of mathematical knowledge in understanding and analyzing issues in decision making. Through an imaginative selection of topics, Aliprantis and Chakrabarti treat decision and game theory as part of one body of knowledge. They move from problems involving the individual decision-maker to progressively more complex problems such as sequential rationality, auctions, and bargaining. By building each chapter on material presented earlier, the authors offer a self-contained and comprehensive treatment of these topics. Successfully class-tested in an advanced undergraduate course at the Krannert School of Management and in a graduate course in economics at Indiana University, Games and Decision Making, Second Edition, is an essential text for advanced undergraduates and graduate students of decision theory and game theory. The book is accessible to students who have a good basic understanding of elementary calculus and probability theory.
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(This monograph is a systematic exposition of the authors'...)
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, 23J or 52J may treat chapter one as a handy reference for the main economic concepts and notions that are used throughout the book.
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(This is one of the few books available in the literature ...)
This is one of the few books available in the literature that contains problems devoted entirely to the theory of operators on Banach spaces and Banach lattices. The book contains complete solutions to the more than 600 exercises in the companion volume, ""An Invitation to Operator Theory"", Volume 50 in the AMS series ""Graduate Studies in Mathematics"", also by Abramovich and Aliprantis. The exercises and solutions contained in this volume serve many purposes.First, they provide an opportunity to the readers to test their understanding of the theory. Second, they are used to demonstrate explicitly technical details in the proofs of many results in operator theory, providing the reader with rigorous and complete accounts of such details. Third, the exercises include many well-known results whose proofs are not readily available elsewhere. Finally, the book contains a considerable amount of additional material and further developments. By adding extra material to many exercises, the authors have managed to keep the presentation as self-contained as possible. The book can be very useful as a supplementary text to graduate courses in operator theory, real analysis, function theory, integration theory, measure theory, and functional analysis. It will also make a nice reference tool for researchers in physics, engineering, economics, and finance.
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( A collection of problems and solutions in real analysis...)
A collection of problems and solutions in real analysis based on the major textbook, Principles of Real Analysis (also by Aliprantis and Burkinshaw), Problems in Real Analysis is the ideal companion for senior science and engineering undergraduates and first-year graduate courses in real analysis. It is intended for use as an independent source, and is an invaluable tool for students who wish to develop a deep understanding and proficiency in the use of integration methods. Problems in Real Analysis teaches the basic methods of proof and problem-solving by presenting the complete solutions to over 600 problems that appear in Principles of Real Analysis, Third Edition. The problems are distributed in forty sections, and cover the entire spectrum of difficulty. • An ideal companion for senior science and engineering undergraduates and first-year graduate courses in real analysis • An invaluable tool for students who wish to develop a deep understanding and proficiency in the use of integration methods • Teaches the basic methods of proof and problem-solving by presenting the complete solutions to over 600 problems
http://www.amazon.com/gp/product/0120502534/?tag=2022091-20
(With the success of its previous editions, Principles of ...)
With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter on Hilbert spaces as well as integrating over 150 new exercises throughout. The new edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the "Daniell Method" and the measure theoretic approach. Students will be challenged by the more than 600 exercises contained in the book. Topics are illustrated by many varied examples, and they provide clear connections between real analysis and functional analysis. • Gives a unique presentation of integration theory • Over 150 new exercises integrated throughout the text • Presents a new chapter on Hilbert Spaces • Provides a rigorous introduction to measure theory • Illustrated with new and varied examples in each chapter • Introduces topological ideas in a friendly manner • Offers a clear connection between real analysis and functional analysis • Includes brief biographies of mathematicians
http://www.amazon.com/gp/product/0120502577/?tag=2022091-20
(This book offers a comprehensive and reader-friendly expo...)
This book offers a comprehensive and reader-friendly exposition of the theory of linear operators on Banach spaces and Banach lattices. Abramovich and Aliprantis give a unique presentation that includes many new developments in operator theory and also draws together results that are spread over the vast literature. For instance, invariant subspaces of positive operators and the Daugavet equation are presented in monograph form for the first time. The authors keep the discussion self-contained and use exercises to achieve this goal. The book contains over 600 exercises to help students master the material developed in the text. The exercises are of varying degrees of difficulty and play an important and useful role in the exposition. They help to free the proofs of the main results of some technical details but provide students with accurate and complete accounts of how such details ought to be worked out.The exercises also contain a considerable amount of additional material that includes many well-known results whose proofs are not readily available elsewhere. The companion volume, ""Problems in Operator Theory"", also by Abramovich and Aliprantis, is available from the AMS as Volume 51 in the ""Graduate Studies in Mathematics"" series, and it contains complete solutions to all exercises in ""An Invitation to Operator Theory"". The solutions demonstrate explicitly technical details in the proofs of many results in operator theory, providing the reader with rigorous and complete accounts of such details. Finally, the book offers a considerable amount of additional material and further developments.By adding extra material to many exercises, the authors have managed to keep the presentation as self-contained as possible. The best way of learning mathematics is by doing mathematics, and the book ""Problems in Operator Theory"" will help achieve this goal. Prerequisites to each book are the standard introductory graduate courses in real analysis, general topology, measure theory, and functional analysis. ""An Invitation to Operator Theory"" is suitable for graduate or advanced courses in operator theory, real analysis, integration theory, measure theory, function theory, and functional analysis. ""Problems in Operator Theory"" is a very useful supplementary text in the above areas. Both books will be of great interest to researchers and students in mathematics, as well as in physics, economics, finance, engineering, and other related areas, and will make an indispensable reference tool.
http://www.amazon.com/gp/product/0821821466/?tag=2022091-20
(This is the first book to teach the basic methods of proo...)
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.
http://www.amazon.com/gp/product/3642082378/?tag=2022091-20
economist educator mathematician
Aliprantis, Charalambos Dionisios was born on May 12, 1946 in Cephalonia, Greece. Came to United States, 1969. Son of Dionisios Elias and Sofronia Aliprantis.
Diploma in Mathematics, University Athens, 1968. Master of Science in Mathematics, California Institute of Technology, Pasadena, 1971. Doctor of Philosophy in Mathematics, California Institute of Technology, Pasadena, 1973.
Teaching assistant, U. Athens, 1969;
graduate teaching assistant, California Institute Technology, Pasadena, 1969-1973;
instructor, Occidental College, 1973-1974;
assistant professor mathematics, Occidental College, 1974-1975;
assistant professor mathematics, Indiana U.-Purdue University, Indianapolis, 1975-1978;
associate professor mathematics, Indiana U.-Purdue University, Indianapolis, 1978-1981;
professor mathematics, Indiana U.-Purdue University, Indianapolis, since 1981;
professor mathematics and economics, Indiana U.-Purdue University, Indianapolis, 1984-1997;
acting chairman departments mathematics and computer science, Indiana U.-Purdue University, Indianapolis, 1988-1989;
professor economics and mathematics, Purdue University, West Lafayette, Indiana, since 1998. Research scientist STD Research Corporation, Arcadia, California, 1973-1974. Visiting professor.math.
California Institute Technology, spring 1982, visiting professor mathematics and economics, 1989-1990, visiting professor economics, 1996. Visiting associate professor mathematics University of Southern California, 1981. Senior research fellow Institute for Mathematics and its Applications University of Minnesota, 1983.
Visiting professor economics Cornell Univercity, Ithaca, New York, 1996. Speaker infield.
( A collection of problems and solutions in real analysis...)
(With the success of its previous editions, Principles of ...)
(With the success of its previous editions, Principles of ...)
(This is one of the few books available in the literature ...)
(An Invitation to Operator Theory offers a comprehensive a...)
(The volume contains the proceedings of a conference in ma...)
( Reprinted by popular demand, this monograph presents a ...)
(This monograph is a systematic exposition of the authors'...)
(This book offers a comprehensive and reader-friendly expo...)
(This is the first book to teach the basic methods of proo...)
(This is the first book to teach the basic methods of proo...)
( What you’ll find in this monograph is nothing less than...)
(Games and Decision Making, Second Edition, is a unique bl...)
(Riesz space (or a vector lattice) is an ordered vector sp...)
(Will be shipped from US. Used books may not include compa...)
Member of Mathematics Association America, Society Advancement of Economic Theory, American Mathematics Society.
Married Bernadette Aliprantis, August 31, 1974. Children: Claire, Dionissi.