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  • © 1983

Topological Vector Spaces I

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 159)

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  • ISBN: 978-3-642-64988-2
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Table of contents (6 chapters)

  1. Front Matter

    Pages I-XV
  2. Fundamentals of General Topology

    • Gottfried Köthe
    Pages 1-47
  3. Vector Spaces over General Fields

    • Gottfried Köthe
    Pages 48-122
  4. Topological Vector Spaces

    • Gottfried Köthe
    Pages 123-201
  5. Locally Convex Spaces. Fundamentals

    • Gottfried Köthe
    Pages 202-294
  6. Some Special Classes of Locally Convex Spaces

    • Gottfried Köthe
    Pages 367-436
  7. Back Matter

    Pages 437-456

About this book

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.

Keywords

  • Convexity
  • Natural
  • Smooth function
  • Spaces
  • Topologischer Raum
  • Vector
  • algebra
  • banach spaces
  • compactness
  • convergence
  • holomorphic function
  • linear algebra
  • metric space
  • proof
  • topological vector space

Authors and Affiliations

  • Institut für angewandte Mathematik, Johann-Wolfgang-Goethe-Universität, Frankfurt am Main, Germany

    Gottfried Köthe

Bibliographic Information

  • Book Title: Topological Vector Spaces I

  • Authors: Gottfried Köthe

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-64988-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin, Heidelberg 1983

  • Softcover ISBN: 978-3-642-64990-5

  • eBook ISBN: 978-3-642-64988-2

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XVI, 456

  • Additional Information: Vol. 2 published as Band 237 of the same series; original German edition published as Band 107 of the same series

  • Topics: Analysis

Buying options

eBook USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-3-642-64988-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 149.99
Price excludes VAT (USA)