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Free Topological Vector Spaces
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Book Synopsis Topological Vector Spaces and Distributions by : John Horvath
Download or read book Topological Vector Spaces and Distributions written by John Horvath and published by Courier Corporation. This book was released on 2013-10-03 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Precise exposition provides an excellent summary of the modern theory of locally convex spaces and develops the theory of distributions in terms of convolutions, tensor products, and Fourier transforms. 1966 edition.
Book Synopsis A Course on Topological Vector Spaces by : Jürgen Voigt
Download or read book A Course on Topological Vector Spaces written by Jürgen Voigt and published by Springer Nature. This book was released on 2020-03-06 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the theory of topological vector spaces, with a focus on locally convex spaces. It discusses topologies in dual pairs, culminating in the Mackey-Arens theorem, and also examines the properties of the weak topology on Banach spaces, for instance Banach’s theorem on weak*-closed subspaces on the dual of a Banach space (alias the Krein-Smulian theorem), the Eberlein-Smulian theorem, Krein’s theorem on the closed convex hull of weakly compact sets in a Banach space, and the Dunford-Pettis theorem characterising weak compactness in L1-spaces. Lastly, it addresses topics such as the locally convex final topology, with the application to test functions D(Ω) and the space of distributions, and the Krein-Milman theorem. The book adopts an “economic” approach to interesting topics, and avoids exploring all the arising side topics. Written in a concise mathematical style, it is intended primarily for advanced graduate students with a background in elementary functional analysis, but is also useful as a reference text for established mathematicians.
Book Synopsis Topological Vector Spaces by : N. Bourbaki
Download or read book Topological Vector Spaces written by N. Bourbaki and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a softcover reprint of the 1987 English translation of the second edition of Bourbaki's Espaces Vectoriels Topologiques. Much of the material has been rearranged, rewritten, or replaced by a more up-to-date exposition, and a good deal of new material has been incorporated in this book, reflecting decades of progress in the field.
Book Synopsis Topological Vector Spaces by : Lawrence Narici
Download or read book Topological Vector Spaces written by Lawrence Narici and published by CRC Press. This book was released on 2010-07-26 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: With many new concrete examples and historical notes, Topological Vector Spaces, Second Edition provides one of the most thorough and up-to-date treatments of the Hahn-Banach theorem. This edition explores the theorem's connection with the axiom of choice, discusses the uniqueness of Hahn-Banach extensions, and includes an entirely new chapter on v
Book Synopsis Topological Vector Spaces and Their Applications by : V.I. Bogachev
Download or read book Topological Vector Spaces and Their Applications written by V.I. Bogachev and published by Springer. This book was released on 2017-05-16 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Free Topological Vector Spaces by : Joe Flood
Download or read book Free Topological Vector Spaces written by Joe Flood and published by . This book was released on 1984 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Counterexamples in Topological Vector Spaces by : S.M. Khaleelulla
Download or read book Counterexamples in Topological Vector Spaces written by S.M. Khaleelulla and published by Springer. This book was released on 2006-11-17 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Locally Convex Spaces written by and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book grew out of several courses which I have taught at the University of Zürich and at the University of Maryland during the past seven years. It is primarily intended to be a systematic text on locally convex spaces at the level of a student who has some familiarity with general topology and basic measure theory. However, since much of the material is of fairly recent origin and partly appears here for the first time in a book, and also since some well-known material has been given a not so well-known treatment, I hope that this book might prove useful even to more advanced readers. And in addition I hope that the selection ofmaterial marks a sufficient set-offfrom the treatments in e.g. N. Bourbaki [4], [5], R.E. Edwards [1], K. Floret-J. Wloka [1], H.G. Garnir-M. De Wilde-J. Schmets [1], AGrothendieck [13], H. Heuser [1], J. Horvath [1], J.L. Kelley-I. Namioka et al. [1], G. Köthe [7], [10], A P. Robertson W. Robertson [1], W. Rudin [2], H.H. Schaefer [1], F. Treves [l], A Wilansky [1]. A few sentences should be said about the organization of the book. It consists of 21 chapters which are grouped into three parts. Each chapter splits into several sections. Chapters, sections, and the statements therein are enumerated in consecutive fashion.
Author :Alexander Arhangel’skii Publisher :Springer Science & Business Media ISBN 13 :949121635X Total Pages :794 pages Book Rating :4.4/5 (912 download)
Book Synopsis Topological Groups and Related Structures, An Introduction to Topological Algebra. by : Alexander Arhangel’skii
Download or read book Topological Groups and Related Structures, An Introduction to Topological Algebra. written by Alexander Arhangel’skii and published by Springer Science & Business Media. This book was released on 2008-05-01 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately.
Book Synopsis Linear Topological Spaces by : John L Kelley
Download or read book Linear Topological Spaces written by John L Kelley and published by Hassell Street Press. This book was released on 2021-09-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Book Synopsis Locally Convex Spaces by : M. Scott Osborne
Download or read book Locally Convex Spaces written by M. Scott Osborne and published by Springer Science & Business Media. This book was released on 2013-11-08 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convex topological vector spaces, is intended to cover most of the general theory needed for application to other areas of analysis. Normed vector spaces, Banach spaces, and Hilbert spaces are all examples of classes of locally convex spaces, which is why this is an important topic in functional analysis. While this graduate text focuses on what is needed for applications, it also shows the beauty of the subject and motivates the reader with exercises of varying difficulty. Key topics covered include point set topology, topological vector spaces, the Hahn–Banach theorem, seminorms and Fréchet spaces, uniform boundedness, and dual spaces. The prerequisite for this text is the Banach space theory typically taught in a beginning graduate real analysis course.
Book Synopsis Topological Vector Spaces, Distributions and Kernels by : François Treves
Download or read book Topological Vector Spaces, Distributions and Kernels written by François Treves and published by Elsevier. This book was released on 2016-06-03 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological Vector Spaces, Distributions and Kernels discusses partial differential equations involving spaces of functions and space distributions. The book reviews the definitions of a vector space, of a topological space, and of the completion of a topological vector space. The text gives examples of Frechet spaces, Normable spaces, Banach spaces, or Hilbert spaces. The theory of Hilbert space is similar to finite dimensional Euclidean spaces in which they are complete and carry an inner product that can determine their properties. The text also explains the Hahn-Banach theorem, as well as the applications of the Banach-Steinhaus theorem and the Hilbert spaces. The book discusses topologies compatible with a duality, the theorem of Mackey, and reflexivity. The text describes nuclear spaces, the Kernels theorem and the nuclear operators in Hilbert spaces. Kernels and topological tensor products theory can be applied to linear partial differential equations where kernels, in this connection, as inverses (or as approximations of inverses), of differential operators. The book is suitable for vector mathematicians, for students in advanced mathematics and physics.
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 Topology and Maps written by T. Husain and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is suitable for undergraduate students as well as advanced students and research workers. It consists of ten chapters, the first six of which are meant for beginners and are therefore suitable for undergraduate students; Chapters VII-X are suitable for advanced students and research workers interested in functional analysis. This book has two special features: First, it contains generalizations of continuous maps on topological spaces, e. g. , almost continuous maps, nearly continuous maps, maps with closed graph, graphically continuous maps, w-continuous maps, and a-continuous maps, etc. and some of their properties. The treatment of these notions appears here, in Chapter VII, for the first time in book form. The second feature consists in some not-so-easily-available nuptial delights that grew out of the marriage of topology and functional analysis; they are topics mainly courted by functional analysts and seldom given in topology books. Specifically, one knows that the set C(X) of all real- or com plex-valued continuous functions on a completely regular space X forms a locally convex topological algebra, a fortiori a topological vector space, in the compact-open topology. A number of theorems are known: For example, C(X) is a Banach space iff X is compact, or C(X) is complete iff X is a kr-space, and so on. Chapters VIII and X include this material, which, to the regret of many interested readers has not previously been available in book form (a recent publication (Weir [\06]) does, however, contain some material of our Chapter X).
Book Synopsis Calculus on Normed Vector Spaces by : Rodney Coleman
Download or read book Calculus on Normed Vector Spaces written by Rodney Coleman and published by Springer Science & Business Media. This book was released on 2012-07-25 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematical maturity. All the important topology and functional analysis topics are introduced where necessary. In its attempt to show how calculus on normed vector spaces extends the basic calculus of functions of several variables, this book is one of the few textbooks to bridge the gap between the available elementary texts and high level texts. The inclusion of many non-trivial applications of the theory and interesting exercises provides motivation for the reader.
Book Synopsis Optimization by Vector Space Methods by : David G. Luenberger
Download or read book Optimization by Vector Space Methods written by David G. Luenberger and published by John Wiley & Sons. This book was released on 1997-01-23 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.
Book Synopsis Handbook of Analysis and Its Foundations by : Eric Schechter
Download or read book Handbook of Analysis and Its Foundations written by Eric Schechter and published by Academic Press. This book was released on 1996-10-24 with total page 907 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/
