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Riesz Spaces
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Book Synopsis Locally Solid Riesz Spaces with Applications to Economics by : Charalambos D. Aliprantis
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.
Book Synopsis Introduction to Operator Theory in Riesz Spaces by : Adriaan C. Zaanen
Download or read book Introduction to Operator Theory in Riesz Spaces written by Adriaan C. Zaanen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the beginning of the thirties a considerable number of books on func tional analysis has been published. Among the first ones were those by M. H. Stone on Hilbert spaces and by S. Banach on linear operators, both from 1932. The amount of material in the field of functional analysis (in cluding operator theory) has grown to such an extent that it has become impossible now to include all of it in one book. This holds even more for text books. Therefore, authors of textbooks usually restrict themselves to normed spaces (or even to Hilbert space exclusively) and linear operators in these spaces. In more advanced texts Banach algebras and (or) topological vector spaces are sometimes included. It is only rarely, however, that the notion of order (partial order) is explicitly mentioned (even in more advanced exposi tions), although order structures occur in a natural manner in many examples (spaces of real continuous functions or spaces of measurable function~). This situation is somewhat surprising since there exist important and illuminating results for partially ordered vector spaces, in . particular for the case that the space is lattice ordered. Lattice ordered vector spaces are called vector lattices or Riesz spaces. The first results go back to F. Riesz (1929 and 1936), L. Kan torovitch (1935) and H. Freudenthal (1936).
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
Book Synopsis Topological Riesz Spaces and Measure Theory by : D. H. Fremlin
Download or read book Topological Riesz Spaces and Measure Theory written by D. H. Fremlin and published by Cambridge University Press. This book was released on 2008-11-20 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measure Theory has played an important part in the development of functional analysis: it has been the source of many examples for functional analysis, including some which have been leading cases for major advances in the general theory, and certain results in measure theory have been applied to prove general results in analysis. Often the ordinary functional analyst finds the language and a style of measure theory a stumbling block to a full understanding of these developments. Dr Fremlin's aim in writing this book is therefore 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. Thus this book gathers together material which is not readily available elsewhere in a single collection and presents it in a form accessible to the first-year graduate student, whose knowledge of measure theory need not have progressed beyond that of the ordinary lebesgue integral.
Download or read book Riesz Spaces written by W.A.J. Luxemburg and published by Elsevier. This book was released on 2000-04-01 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: Riesz Spaces
Book Synopsis Riesz Spaces by : Adriaan Cornelis Zaanen
Download or read book Riesz Spaces written by Adriaan Cornelis Zaanen and published by Elsevier. This book was released on 1971 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Charalambos D. Aliprantis Publisher :Springer Science & Business Media ISBN 13 :3642581994 Total Pages :231 pages Book Rating :4.6/5 (425 download)
Book Synopsis Positive Operators, Riesz Spaces, and Economics by : Charalambos D. Aliprantis
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 Riesz Spaces II written by A.C. Zaanen and published by Elsevier. This book was released on 1983-05-01 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt: While Volume I (by W.A.J. Luxemburg and A.C. Zaanen, NHML Volume 1, 1971) is devoted to the algebraic aspects of the theory, this volume emphasizes the analytical theory of Riesz spaces and operators between these spaces. Though the numbering of chapters continues on from the first volume, this does not imply that everything covered in Volume I is required for this volume, however the two volumes are to some extent complementary.
Book Synopsis Kurzweil-Henstock Integral in Riesz spaces by : Antonio Boccuto
Download or read book Kurzweil-Henstock Integral in Riesz spaces written by Antonio Boccuto and published by Bentham Science Publishers. This book was released on 2010-04-02 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This Ebook is concerned with both the theory of the Kurzweil-Henstock integral and the basic facts on Riesz spaces. Moreover, even the so-called Sipos integral, which has several applications in economy, is illustrated. The aim of this Ebook is two-fold. "
Book Synopsis An Introduction to Frames and Riesz Bases by : Ole Christensen
Download or read book An Introduction to Frames and Riesz Bases written by Ole Christensen and published by Birkhäuser. This book was released on 2016-05-24 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and expanded monograph presents the general theory for frames and Riesz bases in Hilbert spaces as well as its concrete realizations within Gabor analysis, wavelet analysis, and generalized shift-invariant systems. Compared with the first edition, more emphasis is put on explicit constructions with attractive properties. Based on the exiting development of frame theory over the last decade, this second edition now includes new sections on the rapidly growing fields of LCA groups, generalized shift-invariant systems, duality theory for as well Gabor frames as wavelet frames, and open problems in the field. Key features include: *Elementary introduction to frame theory in finite-dimensional spaces * Basic results presented in an accessible way for both pure and applied mathematicians * Extensive exercises make the work suitable as a textbook for use in graduate courses * Full proofs includ ed in introductory chapters; only basic knowledge of functional analysis required * Explicit constructions of frames and dual pairs of frames, with applications and connections to time-frequency analysis, wavelets, and generalized shift-invariant systems * Discussion of frames on LCA groups and the concrete realizations in terms of Gabor systems on the elementary groups; connections to sampling theory * Selected research topics presented with recommendations for more advanced topics and further readin g * Open problems to stimulate further research An Introduction to Frames and Riesz Bases will be of interest to graduate students and researchers working in pure and applied mathematics, mathematical physics, and engineering. Professionals working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find this book a useful self-study reference. Review of the first edition: "Ole Christensen’s An Introduction to Frames and Riesz Bases is a first-rate introduction to the field ... . The book provides an excellent exposition of these topics. The material is broad enough to pique the interest of many readers, the included exercises supply some interesting challenges, and the coverage provides enough background for those new to the subject to begin conducting original research." — Eric S. Weber, American Mathematical Monthly, Vol. 112, February, 2005
Book Synopsis Bochner-Riesz Means on Euclidean Spaces by : Shanzhen Lu
Download or read book Bochner-Riesz Means on Euclidean Spaces written by Shanzhen Lu and published by World Scientific. This book was released on 2013 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book mainly deals with the BochnerOCoRiesz means of multiple Fourier integral and series on Euclidean spaces. It aims to give a systematical introduction to the fundamental theories of the BochnerOCoRiesz means and important achievements attained in the last 50 years. For the BochnerOCoRiesz means of multiple Fourier integral, it includes the Fefferman theorem which negates the Disc multiplier conjecture, the famous Carleson-SjAlin theorem, and Carbery-Rubio de Francia-Vega's work on almost everywhere convergence of the BochnerOCoRiesz means below the critical index. For the BochnerOCoRiesz means of multiple Fourier series, it includes the theory and application of a class of function space generated by blocks, which is closely related to almost everywhere convergence of the BochnerOCoRiesz means. In addition, the book also introduce some research results on approximation of functions by the BochnerOCoRiesz means.
Book Synopsis Measure, Integration and Function Spaces by : Charles Swartz
Download or read book Measure, Integration and Function Spaces written by Charles Swartz and published by World Scientific. This book was released on 1994 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text contains a basic introduction to the abstract measure theory and the Lebesgue integral. Most of the standard topics in the measure and integration theory are discussed. In addition, topics on the Hewitt-Yosida decomposition, the Nikodym and Vitali-Hahn-Saks theorems and material on finitely additive set functions not contained in standard texts are explored. There is an introductory section on functional analysis, including the three basic principles, which is used to discuss many of the classic Banach spaces of functions and their duals. There is also a chapter on Hilbert space and the Fourier transform.
Book Synopsis Fractal Approaches for Modeling Financial Assets and Predicting Crises by : Nekrasova, Inna
Download or read book Fractal Approaches for Modeling Financial Assets and Predicting Crises written by Nekrasova, Inna and published by IGI Global. This book was released on 2018-02-09 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an ever-changing economy, market specialists strive to find new ways to evaluate the risks and potential reward of economic ventures. They start by assessing the importance of human reaction during the economic planning process and put together systems to measure financial markets and their longevity. Fractal Approaches for Modeling Financial Assets and Predicting Crises is a critical scholarly resource that examines the fractal structure and long-term memory of the financial markets in order to predict prices of financial assets and financial crises. Featuring coverage on a broad range of topics, such as computational process models, chaos theory, and game theory, this book is geared towards academicians, researchers, and students seeking current research on pricing and predicting financial crises.
Book Synopsis Ordered Linear Spaces by : Graham Jameson
Download or read book Ordered Linear Spaces written by Graham Jameson and published by Springer. This book was released on 2006-11-15 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Encyclopaedia of Mathematics by : M. Hazewinkel
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Uniform Spaces and Measures by : Jan Pachl
Download or read book Uniform Spaces and Measures written by Jan Pachl and published by Springer Science & Business Media. This book was released on 2012-10-16 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the need for an accessible comprehensive exposition of the theory of uniform measures; the need that became more critical when recently uniform measures reemerged in new results in abstract harmonic analysis. Until now, results about uniform measures have been scattered through many papers written by a number of authors, some unpublished, written using a variety of definitions and notations. Uniform measures are certain functionals on the space of bounded uniformly continuous functions on a uniform space. They are a common generalization of several classes of measures and measure-like functionals studied in abstract and topological measure theory, probability theory, and abstract harmonic analysis. They offer a natural framework for results about topologies on spaces of measures and about the continuity of convolution of measures on topological groups and semitopological semigroups. The book is a reference for the theory of uniform measures. It includes a self-contained development of the theory with complete proofs, starting with the necessary parts of the theory of uniform spaces. It presents diverse results from many sources organized in a logical whole, and includes several new results. The book is also suitable for graduate or advanced undergraduate courses on selected topics in topology and functional analysis. The text contains a number of exercises with solution hints, and four problems with suggestions for further research.
Book Synopsis Recent Applications of Financial Risk Modelling and Portfolio Management by : Škrinjari?, Tihana
Download or read book Recent Applications of Financial Risk Modelling and Portfolio Management written by Škrinjari?, Tihana and published by IGI Global. This book was released on 2020-09-25 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: In today’s financial market, portfolio and risk management are facing an array of challenges. This is due to increasing levels of knowledge and data that are being made available that have caused a multitude of different investment models to be explored and implemented. Professionals and researchers in this field are in need of up-to-date research that analyzes these contemporary models of practice and keeps pace with the advancements being made within financial risk modelling and portfolio control. Recent Applications of Financial Risk Modelling and Portfolio Management is a pivotal reference source that provides vital research on the use of modern data analysis as well as quantitative methods for developing successful portfolio and risk management techniques. While highlighting topics such as credit scoring, investment strategies, and budgeting, this publication explores diverse models for achieving investment goals as well as improving upon traditional financial modelling methods. This book is ideally designed for researchers, financial analysts, executives, practitioners, policymakers, academicians, and students seeking current research on contemporary risk management strategies in the financial sector.
