Additive Subgroups of Topological Vector Spaces
| Author | : Wojciech Banaszczyk |
| Publisher | : |
| Total Pages | : 192 |
| Release | : 2014-01-15 |
| Genre | : |
| ISBN | : 9783662215265 |
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Additive Subgroups Of Topological Vector Spaces
Download Additive Subgroups Of Topological Vector Spaces full books in PDF, epub, and Kindle. Read online free Additive Subgroups Of Topological Vector Spaces ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Additive Subgroups of Topological Vector Spaces
| Author | : Wojciech Banaszczyk |
| Publisher | : Springer |
| Total Pages | : 185 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540463968 |
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The Pontryagin-van Kampen duality theorem and the Bochner theorem on positive-definite functions are known to be true for certain abelian topological groups that are not locally compact. The book sets out to present in a systematic way the existing material. It is based on the original notion of a nuclear group, which includes LCA groups and nuclear locally convex spaces together with their additive subgroups, quotient groups and products. For (metrizable, complete) nuclear groups one obtains analogues of the Pontryagin duality theorem, of the Bochner theorem and of the Lévy-Steinitz theorem on rearrangement of series (an answer to an old question of S. Ulam). The book is written in the language of functional analysis. The methods used are taken mainly from geometry of numbers, geometry of Banach spaces and topological algebra. The reader is expected only to know the basics of functional analysis and abstract harmonic analysis.
Topological Vector Spaces
| Author | : Lawrence Narici |
| Publisher | : CRC Press |
| Total Pages | : 628 |
| Release | : 2010-07-26 |
| Genre | : Mathematics |
| ISBN | : 1584888679 |
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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
Topological Vector Spaces and Algebras
| Author | : Lucien Waelbroeck |
| Publisher | : Springer |
| Total Pages | : 165 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540369384 |
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The lectures associated with these notes were given at the Instituto de Matematica Pura e Aplicada (IMPA) in Rio de Janeiro, during the local winter 1970. To emphasize the properties of topological algebras, the author had started out his lecture with results about topological algebras, and introduced the linear results as he went along.
Topological Vector Spaces
| Author | : Alex P. Robertson |
| Publisher | : CUP Archive |
| Total Pages | : 186 |
| Release | : 1980 |
| Genre | : Mathematics |
| ISBN | : 9780521298827 |
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Topological Vector Spaces I
| Author | : Gottfried Köthe |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 470 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642649882 |
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It is the author's aim to give a systematic account of the most im portant ideas, methods and results of the theory of topological vector spaces. After a rapid development during the last 15 years, this theory has now achieved a form which makes such an account seem both possible and desirable. This present first volume begins with the fundamental ideas of general topology. These are of crucial importance for the theory that follows, and so it seems necessary to give a concise account, giving complete proofs. This also has the advantage that the only preliminary knowledge required for reading this book is of classical analysis and set theory. In the second chapter, infinite dimensional linear algebra is considered in comparative detail. As a result, the concept of dual pair and linear topologies on vector spaces over arbitrary fields are intro duced in a natural way. It appears to the author to be of interest to follow the theory of these linearly topologised spaces quite far, since this theory can be developed in a way which closely resembles the theory of locally convex spaces. It should however be stressed that this part of chapter two is not needed for the comprehension of the later chapters. Chapter three is concerned with real and complex topological vector spaces. The classical results of Banach's theory are given here, as are fundamental results about convex sets in infinite dimensional spaces.
Abelian Groups, Module Theory, and Topology
| Author | : Dikran Dikranjan |
| Publisher | : CRC Press |
| Total Pages | : 468 |
| Release | : 2019-05-16 |
| Genre | : Mathematics |
| ISBN | : 1482276054 |
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Features a stimulating selection of papers on abelian groups, commutative and noncommutative rings and their modules, and topological groups. Investigates currently popular topics such as Butler groups and almost completely decomposable groups.
Stereotype Spaces and Algebras
| Author | : Sergei S. Akbarov |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 794 |
| Release | : 2022-08-22 |
| Genre | : Mathematics |
| ISBN | : 3110780917 |
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The term "stereotype space" was introduced in 1995 and is used for a category of locally convex spaces with surprisingly elegant properties. In particular, it consists of spaces reflexive in the sense of Pontryagin, and at the same time it is very wide, since it contains all Fréchet spaces. Its study gives an unexpected point of view on functional analysis that brings this field closer to other main branches of mathematics, namely, to algebra and geometry.
Functional Analysis and Continuous Optimization
| Author | : José M. Amigó |
| Publisher | : Springer Nature |
| Total Pages | : 273 |
| Release | : 2023-07-01 |
| Genre | : Mathematics |
| ISBN | : 3031300149 |
Download Functional Analysis and Continuous Optimization Book in PDF, Epub and Kindle
The book includes selected contributions presented at the "International Meeting on Functional Analysis and Continuous Optimization" held in Elche (Spain) on June 16–17, 2022. Its contents cover very recent results in functional analysis, continuous optimization and the interplay between these disciplines. Therefore, this book showcases current research on functional analysis and optimization with individual contributions, as well as new developments in both areas. As a result, the reader will find useful information and stimulating ideas.
Recent Progress in General Topology II
| Author | : M. Husek |
| Publisher | : Elsevier |
| Total Pages | : 651 |
| Release | : 2002-11-13 |
| Genre | : Mathematics |
| ISBN | : 0080929958 |
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The book presents surveys describing recent developments in most of the primary subfields ofGeneral Topology and its applications to Algebra and Analysis during the last decade. It follows freelythe previous edition (North Holland, 1992), Open Problems in Topology (North Holland, 1990) and Handbook of Set-Theoretic Topology (North Holland, 1984). The book was prepared inconnection with the Prague Topological Symposium, held in 2001. During the last 10 years the focusin General Topology changed and therefore the selection of topics differs slightly from thosechosen in 1992. The following areas experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (includingInfinite-Dimensional Topology and the Geometry of Banach Spaces). Of course, not every important topic could be included in this book. Except surveys, the book contains several historical essays written by such eminent topologists as:R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardeŝić, J. Nagata, M.E. Rudin, J.M. Smirnov (several reminiscences of L. Vietoris are added). In addition to extensive author and subject indexes, a list of all problems and questions posed in this book are added. List of all authors of surveys: A. Arhangel'skii, J. Baker and K. Kunen, H. Bennett and D. Lutzer, J. Dijkstra and J. van Mill, A. Dow, E. Glasner, G. Godefroy, G. Gruenhage, N. Hindman and D. Strauss, L. Hola and J. Pelant, K. Kawamura, H.-P. Kuenzi, W. Marciszewski, K. Martin and M. Mislove and M. Reed, R. Pol and H. Torunczyk, D. Repovs and P. Semenov, D. Shakhmatov, S. Solecki, M. Tkachenko.
