Topological Vector Spaces

Topological Vector Spaces

PRELIMINARY TEXT : DO NOT USE This book is intended to be a systematic text on topological vector spaces and presupposes familiarity with the elements of general topology and linear algebra.

Author: H.H. Schaefer

Publisher: Springer Science & Business Media

ISBN: 0387987266

Category: Mathematics

Page: 346

View: 312

PRELIMINARY TEXT : DO NOT USE This book is intended to be a systematic text on topological vector spaces and presupposes familiarity with the elements of general topology and linear algebra. Each of the chapters is preceded by an introduction and followed by exercises. These exercises are devoted to further results and supplements, in particular, to examples and counter-examples. Hints have been given where it seemed appropriate. This second edition has been thoroughly revised and includes a new chapter on C^* and W^* algebras.
Categories: Mathematics

Topological Vector Spaces Algebras and Related Areas

Topological Vector Spaces  Algebras and Related Areas

This volume contains the proceedings of an international conference held to mark the retirement of Professor Taqdir Husain from McMaster University.

Author: A Lau

Publisher: CRC Press

ISBN: 0582257778

Category: Mathematics

Page: 280

View: 590

This volume contains the proceedings of an international conference held to mark the retirement of Professor Taqdir Husain from McMaster University. The contributions, covering topics such as topological vector spaces, topological algebras and related areas, reflect Husain's research interests and present surveys and new research in the topics of the conference.
Categories: Mathematics

Topological Vector Spaces

Topological Vector Spaces

This is a softcover reprint of the 1987 English translation of the second edition of Bourbaki's Espaces Vectoriels Topologiques.

Author: N. Bourbaki

Publisher: Boom Koninklijke Uitgevers

ISBN: 3540423389

Category: Mathematics

Page: 362

View: 380

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.
Categories: Mathematics

Topological Vector Spaces and Distributions

Topological Vector Spaces and Distributions

Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers.

Author: John Horvath

Publisher: Courier Corporation

ISBN: 9780486311036

Category: Mathematics

Page: 464

View: 590

"The most readable introduction to the theory of vector spaces available in English and possibly any other language."—J. L. B. Cooper, MathSciNet Review Mathematically rigorous but user-friendly, this classic treatise discusses major modern contributions to the field of topological vector spaces. The self-contained treatment includes complete proofs for all necessary results from algebra and topology. Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers. The precise exposition of the first three chapters—covering Banach spaces, locally convex spaces, and duality—provides an excellent summary of the modern theory of locally convex spaces. The fourth and final chapter develops the theory of distributions in relation to convolutions, tensor products, and Fourier transforms. Augmented with many examples and exercises, the text includes an extensive bibliography.
Categories: Mathematics

Modern Methods in Topological Vector Spaces

Modern Methods in Topological Vector Spaces

"Designed for a one-year course in topological vector spaces, this text is geared toward beginning graduate students of mathematics.

Author: Albert Wilansky

Publisher: Courier Corporation

ISBN: 9780486493534

Category: Mathematics

Page: 298

View: 337

"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"--
Categories: Mathematics

Additive Subgroups of Topological Vector Spaces

Additive Subgroups of Topological Vector Spaces

The book sets out to present in a systematic way the existing material.

Author: Wojciech Banaszczyk

Publisher: Springer

ISBN: 9783540463962

Category: Mathematics

Page: 182

View: 842

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.
Categories: Mathematics

Topological Vector Spaces I

Topological Vector Spaces I

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.

Author: Gottfried Köthe

Publisher: Springer

ISBN: 3642649904

Category: Mathematics

Page: 456

View: 909

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.
Categories: Mathematics

Topological Vector Spaces

Topological Vector Spaces

Intended as a systematic text on topological vector spaces, this text assumes familiarity with the elements of general topology and linear algebra.

Author: H.H. Schaefer

Publisher: Springer

ISBN: 146127155X

Category: Mathematics

Page: 349

View: 994

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.
Categories: Mathematics

Topological Vector Spaces

Topological Vector Spaces

Intended as a systematic text on topological vector spaces, this text assumes familiarity with the elements of general topology and linear algebra.

Author: Helmut H. Schaefer

Publisher: Springer Science & Business Media

ISBN: UVA:X001473939

Category: Mathematics

Page: 294

View: 224

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.
Categories: Mathematics

Summer School on Topological Vector Spaces

Summer School on Topological Vector Spaces

L. Waelbroeck, Topological Vector Spaces and Algebras. VII, 158 pages. 1971. DM 16– Vol. 231: H. Reiter, Li-Algebras and Segal Algebras. XI, 113 pages. 1971. DM 16,Vol. 232. T. H. Ganelius, Tauberian Remainder Theorems. VI, 75 pages.

Author: L. Waelbroeck

Publisher: Springer

ISBN: 9783540469773

Category: Mathematics

Page: 232

View: 355

Proceedings 1972
Categories: Mathematics

Topological Vector Spaces

Topological Vector Spaces

Measure and Category. 2nd ed. SCHAEFFER. Topological Vector Spaces. HILTON/STAMMBACH. A Course in Homological Algebra. MACLANE. Categories for the Working Mathematician. HUGHES/PIPER. Projective Planes. SERRE. A Course in Arithmetic.

Author: H.H. Schaefer

Publisher: Springer Science & Business Media

ISBN: 9781468499285

Category: Mathematics

Page: 296

View: 316

The present book is intended to be a systematic text on topological vector spaces and presupposes familiarity with the elements of general topology and linear algebra. The author has found it unnecessary to rederive these results, since they are equally basic for many other areas of mathematics, and every beginning graduate student is likely to have made their acquaintance. Simi larly, the elementary facts on Hilbert and Banach spaces are widely known and are not discussed in detail in this book, which is mainly addressed to those readers who have attained and wish to get beyond the introductory level. The book has its origin in courses given by the author at Washington State University, the University of Michigan, and the University of Tiibingen in the years 1958-1963. At that time there existed no reasonably complete text on topological vector spaces in English, and there seemed to be a genuine need for a book on this subject. This situation changed in 1963 with the appearance of the book by Kelley, Namioka et al. [1] which, through its many elegant proofs, has had some influence on the final draft of this manuscript. Yet the two books appear to be sufficiently different in spirit and subject matter to justify the publication of this manuscript; in particular, the present book includes a discussion of topological tensor products, nuclear spaces, ordered topological vector spaces, and an appendix on positive operators.
Categories: Mathematics

Functional Analysis with Current Applications in Science Technology and Industry

Functional Analysis with Current Applications in Science  Technology and Industry

This volume constitutes the proceedings of a conference on functional analysis and its applications, which took place in India during December 1996.

Author: Martin Brokate

Publisher: CRC Press

ISBN: 0582312604

Category: Mathematics

Page: 359

View: 282

This volume constitutes the proceedings of a conference on functional analysis and its applications, which took place in India during December 1996. Topics include topological vector spaces, Banach algebras, meromorphic functions, partial differential equations, variational equations and inequalities, optimization, wavelets, elastroplasticity, numerical integration, fractal image compression, reservoir simulation, forest management, and industrial maths.
Categories: Mathematics

Eigenfunction Expansions Operator Algebras and Riemannian Symmetric Spaces

Eigenfunction Expansions  Operator Algebras and Riemannian Symmetric Spaces

These are operators which carry a natural space associated with D into its dual. The elements of the range of these eigenprojections are the eigenfunctions, which solve the appropriate eigenvalue equations by duality.

Author: Robert M Kauffman

Publisher: CRC Press

ISBN: 0582276349

Category: Mathematics

Page: 152

View: 882

This Research Note pays particular attention to studying the convergence of the expansion and to the case where D is a family of partial differential operators. All operators in the natural von Neumann algebraassociated with D, and also unbounded operators affiliated with this algebra, are expanded simultaneously in terms of generalized eigenprojections. These are operators which carry a natural space associated with D into its dual. The elements of the range of these eigenprojections are the eigenfunctions, which solve the appropriate eigenvalue equations by duality. The spectral measure is abstractly defined, but its absolute continuity with respect to Hausdorf measure on the joint spectrum is shown to occur when the eigenfunctions are very well-behaved. Uniqueness results are given showing that any two expansions arise from each other by a simple change of variable. A considerable effort has been made to keep the book self-contained for readers with a background in functional analysis including a basic understanding of the theory of von Neumann algebras. More advanced topics in functional analysis, andan introduction to differential geometry and differential operator theory, mostly without proofs, are given in an extensive section on background material.
Categories: Mathematics

Topological Algebras

Topological Algebras

This book discusses general topological algebras; space C(T,F) of continuous functions mapping T into F as an algebra only (with pointwise operations); and C(T,F) endowed with compact-open topology as a topological algebra C(T,F,c).

Author:

Publisher: Elsevier

ISBN: 0080871356

Category: Mathematics

Page: 369

View: 327

This book discusses general topological algebras; space C(T,F) of continuous functions mapping T into F as an algebra only (with pointwise operations); and C(T,F) endowed with compact-open topology as a topological algebra C(T,F,c). It characterizes the maximal ideals and homomorphisms closed maximal ideals and continuous homomorphisms of topological algebras in general and C(T,F,c) in particular. A considerable inroad is made into the properties of C(T,F,c) as a topological vector space. Many of the results about C(T,F,c) serve to illustrate and motivate results about general topological algebras. Attention is restricted to the algebra C(T,R) of real-valued continuous functions and to the pursuit of the maximal ideals and real-valued homomorphisms of such algebras. The chapter presents the correlation of algebraic properties of C(T,F) with purely topological properties of T. The Stone–Čech compactification and the Wallman compactification play an important role in characterizing the maximal ideals of certain topological algebras.
Categories: Mathematics