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Some Aspects Of The Theory Of Riesz Spaces
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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).
Book Synopsis Some Aspects of the Theory of Riesz Spaces by : W. A. J. Luxemburg
Download or read book Some Aspects of the Theory of Riesz Spaces written by W. A. J. Luxemburg and published by . This book was released on 1979 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
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 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:
Book Synopsis Some Aspects of Representation Theory of Riesz Spaces by : Wolfgang Filter
Download or read book Some Aspects of Representation Theory of Riesz Spaces written by Wolfgang Filter and published by . This book was released on 1985 with total page 100 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.
Book Synopsis Riesz Spaces by : Adriaan Cornelis Zaanen
Download or read book Riesz Spaces written by Adriaan Cornelis Zaanen and published by . This book was released on 1983 with total page 0 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 Finite Elements in Vector Lattices by : Martin R. Weber
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.
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 Positive Operators written by and published by Academic Press. This book was released on 1985-10-08 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Positive Operators
Book Synopsis Banach Lattices by : Peter Meyer-Nieberg
Download or read book Banach Lattices written by Peter Meyer-Nieberg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elements of Hilbert Spaces and Operator Theory by : Harkrishan Lal Vasudeva
Download or read book Elements of Hilbert Spaces and Operator Theory written by Harkrishan Lal Vasudeva and published by Springer. This book was released on 2017-03-27 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compression spectrum, have been worked out. Spectral theorems for self-adjoint operators, and normal operators, follow the spectral theorem for compact normal operators. The book also discusses invariant subspaces with special attention to the Volterra operator and unbounded operators. In order to make the text as accessible as possible, motivation for the topics is introduced and a greater amount of explanation than is usually found in standard texts on the subject is provided. The abstract theory in the book is supplemented with concrete examples. It is expected that these features will help the reader get a good grasp of the topics discussed. Hints and solutions to all the problems are collected at the end of the book. Additional features are introduced in the book when it becomes imperative. This spirit is kept alive throughout the book.
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 Operator Algebras, Operator Theory and Applications by : J. J. Grobler
Download or read book Operator Algebras, Operator Theory and Applications written by J. J. Grobler and published by Springer Science & Business Media. This book was released on 2009-12-24 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the eighteenth International Workshop on Operator Theory and Applications (IWOTA), hosted by the Unit for Business Mathematics and Informatics of North-West University, Potchefstroom, South Africa from July 3 to 6, 2007. The conference (as well as these proceedings) was dedicated to Professors Joseph A. Ball and Marinus M. Kaashoek on the occasion of their 60th and 70th birthdays, respectively. This conference had a particular focus on Von Neumann algebras at the interface of operator theory with functional analysis and on applications of operator theory to differential equations.
Author :Charalambos D. Aliprantis Publisher :Springer Science & Business Media ISBN 13 :1402050089 Total Pages :389 pages Book Rating :4.4/5 (2 download)
Book Synopsis Positive Operators by : Charalambos D. Aliprantis
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.
