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Semitopological Vector Spaces
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Book Synopsis Semitopological Vector Spaces by : Mark Burgin
Download or read book Semitopological Vector Spaces written by Mark Burgin and published by CRC Press. This book was released on 2017-06-26 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new volume shows how it is possible to further develop and essentially extend the theory of operators in infinite-dimensional vector spaces, which plays an important role in mathematics, physics, information theory, and control theory. The book describes new mathematical structures, such as hypernorms, hyperseminorms, hypermetrics, semitopological vector spaces, hypernormed vector spaces, and hyperseminormed vector spaces. It develops mathematical tools for the further development of functional analysis and broadening of its applications. Exploration of semitopological vector spaces, hypernormed vector spaces, hyperseminormed vector spaces, and hypermetric vector spaces is the main topic of this book. A new direction in functional analysis, called quantum functional analysis, has been developed based on polinormed and multinormed vector spaces and linear algebras. At the same time, normed vector spaces and topological vector spaces play an important role in physics and in control theory. To make this book comprehendible for the reader and more suitable for students with some basic knowledge in mathematics, denotations and definitions of the main mathematical concepts and structures used in the book are included in the appendix, making the book useful for enhancing traditional courses of calculus for undergraduates, as well as for separate courses for graduate students. The material of Semitopological Vector Spaces: Hypernorms, Hyperseminorms and Operators is closely related to what is taught at colleges and universities. It is possible to use a definite number of statements from the book as exercises for students because their proofs are not given in the book but left for the reader.
Book Synopsis Topological Vector Spaces I by : Gottfried Köthe
Download or read book Topological Vector Spaces I written by Gottfried Köthe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topological Vector Spaces and Algebras by : Lucien Waelbroeck
Download or read book Topological Vector Spaces and Algebras written by Lucien Waelbroeck and published by Springer. This book was released on 2006-11-15 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Topological Vector Spaces by : Gottfried Köthe
Download or read book Topological Vector Spaces written by Gottfried Köthe and published by Springer. This book was released on 1983 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topological Vector Spaces by : Alex P. Robertson
Download or read book Topological Vector Spaces written by Alex P. Robertson and published by CUP Archive. This book was released on 1980 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topological Vector Spaces by : Nicolas Bourbaki
Download or read book Topological Vector Spaces written by Nicolas Bourbaki and published by . This book was released on 1987 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 : Alexandre Grothendieck
Download or read book Topological Vector Spaces written by Alexandre Grothendieck and published by Taylor & Francis Group. This book was released on 1973 with total page 264 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:
Book Synopsis Topological Vector Spaces II by : Gottfried Köthe
Download or read book Topological Vector Spaces II written by Gottfried Köthe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the preface to Volume One I promised a second volume which would contain the theory of linear mappings and special classes of spaces im portant in analysis. It took me nearly twenty years to fulfill this promise, at least to some extent. To the six chapters of Volume One I added two new chapters, one on linear mappings and duality (Chapter Seven), the second on spaces of linear mappings (Chapter Eight). A glance at the Contents and the short introductions to the two new chapters will give a fair impression of the material included in this volume. I regret that I had to give up my intention to write a third chapter on nuclear spaces. It seemed impossible to include the recent deep results in this field without creating a great further delay. A substantial part of this book grew out of lectures I held at the Mathematics Department of the University of Maryland· during the academic years 1963-1964, 1967-1968, and 1971-1972. I would like to express my gratitude to my colleagues J. BRACE, S. GOLDBERG, J. HORVATH, and G. MALTESE for many stimulating and helpful discussions during these years. I am particularly indebted to H. JARCHOW (Ziirich) and D. KEIM (Frankfurt) for many suggestions and corrections. Both have read the whole manuscript. N. ADASCH (Frankfurt), V. EBERHARDT (Miinchen), H. MEISE (Diisseldorf), and R. HOLLSTEIN (Paderborn) helped with important observations.
Book Synopsis Topological Vector Spaces by : Nicolas Bourbaki
Download or read book Topological Vector Spaces written by Nicolas Bourbaki and published by . This book was released on 1987 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topological Vector Spaces by : H.H. Schaefer
Download or read book Topological Vector Spaces written by H.H. Schaefer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended as a systematic text on topological vector spaces, this text assumes familiarity with the elements of general topology and linear algebra. Similarly, the elementary facts on Hilbert and Banach spaces are not discussed in detail here, since the book is mainly addressed to those readers who wish to go beyond the introductory level. Each of the chapters is preceded by an introduction and followed by exercises, which in turn are devoted to further results and supplements, in particular, to examples and counter-examples, and hints have been given where appropriate. This second edition has been thoroughly revised and includes a new chapter on C^* and W^* algebras.
Book Synopsis Modern Methods in Topological Vector Spaces by : Albert Wilansky
Download or read book Modern Methods in Topological Vector Spaces written by Albert Wilansky and published by Courier Corporation. This book was released on 2013-01-01 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Designed for a one-year course in topological vector spaces, this text is geared toward beginning graduate students of mathematics. Topics include Banach space, open mapping and closed graph theorems, local convexity, duality, equicontinuity, operators,inductive limits, and compactness and barrelled spaces. Extensive tables cover theorems and counterexamples. Rich problem sections throughout the book. 1978 edition"--
Book Synopsis Partially Ordered Topological Vector Spaces by : Yau-Chuen Wong
Download or read book Partially Ordered Topological Vector Spaces written by Yau-Chuen Wong and published by Oxford University Press, USA. This book was released on 1973 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topological Vector Spaces by : Helmut H. Schaefer
Download or read book Topological Vector Spaces written by Helmut H. Schaefer and published by . This book was released on 1966 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
