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Topological Vector Spaces

  • Textbook
  • © 1999

Overview

Authors:
  1. H. H. Schaefer

    1. Mathematisches Institut, Eberhard-Karls-Universitat Tübingen, Tübingen, Germany

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  2. M. P. Wolff

    1. Mathematisches Institut, Eberhard-Karls-Universitat Tübingen, Tübingen, Germany

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Graduate Texts in Mathematics (GTM, volume 3)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xii
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  2. Prerequisites

    • H. H. Schaefer, M. P. Wolff
    Pages 1-11

  3. Topological Vector Spaces

    • H. H. Schaefer, M. P. Wolff
    Pages 12-35

  4. Locally Convex Topological Vector Spaces

    • H. H. Schaefer, M. P. Wolff
    Pages 36-72

  5. Linear Mappings

    • H. H. Schaefer, M. P. Wolff
    Pages 73-121

  6. Duality

    • H. H. Schaefer, M. P. Wolff
    Pages 122-202

  7. Order Structures

    • H. H. Schaefer, M. P. Wolff
    Pages 203-257

  8. C* — and W* — Algebras

    • H. H. Schaefer, M. P. Wolff
    Pages 258-305

  9. Back Matter

    Pages 306-349
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Keywords

About this book

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 :plainly 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 Ttibingen in the years 1958-1963. At that time there existed no reasonably ccmplete 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.

Reviews

"The book has firmly established itself both as a superb introduction to the subject and as a very common source of reference. It is beccoming evident that the book itself will only become irrelevant and pale into insignificance when (and if!) the entire subject of topological vector spaces does. An attractive feature of the book is that it is essentially self-contained, and thus perfectly suitable for senior students having a basic training in the area of elementary functional analysis and set-theoretic topology. My view - let even possibly biased for sentimental resasons - is that the book under review would make for a very practical and useful addition to every matahemtaician's personal office collection."
Vladimir Pestov in Nesletter of the New Zealand Mathematical Society, August 2000

Second Edition

H.H. Schaefer and M.P. Wolff

Topological Vector Spaces

"The reliable textbook, highly esteemed by several generations of students since its first edition in 1966 . . . The book contains a large number of interesting exercises . . . the book of Schaefer and Wolff is worth reading."—ZENTRALBLATT MATH

Authors and Affiliations

  • Mathematisches Institut, Eberhard-Karls-Universitat Tübingen, Tübingen, Germany

    H. H. Schaefer, M. P. Wolff

Bibliographic Information

  • Book Title: Topological Vector Spaces

  • Authors: H. H. Schaefer, M. P. Wolff

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-1468-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1999

  • Hardcover ISBN: 978-0-387-98726-2Published: 24 June 1999

  • Softcover ISBN: 978-1-4612-7155-0Published: 27 September 2012

  • eBook ISBN: 978-1-4612-1468-7Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: XII, 349

  • Topics: Analysis

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