Grundlehren der mathematischen Wissenschaften

Topological Vector Spaces I

Authors: Köthe, Gottfried

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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.

Table of contents (6 chapters)

  • Fundamentals of General Topology

    Köthe, Prof. Dr. Dr. h.c. Gottfried

    Pages 1-47

  • Vector Spaces over General Fields

    Köthe, Prof. Dr. Dr. h.c. Gottfried

    Pages 48-122

  • Topological Vector Spaces

    Köthe, Prof. Dr. Dr. h.c. Gottfried

    Pages 123-201

  • Locally Convex Spaces. Fundamentals

    Köthe, Prof. Dr. Dr. h.c. Gottfried

    Pages 202-294

  • Topological and Geometrical Properties of Locally Convex Spaces

    Köthe, Prof. Dr. Dr. h.c. Gottfried

    Pages 295-366

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-642-64988-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
  • ISBN 978-3-642-64990-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Topological Vector Spaces I
Authors
Translated by
Garling, D.J.H.
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
159
Copyright
1983
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin, Heidelberg
eBook ISBN
978-3-642-64988-2
DOI
10.1007/978-3-642-64988-2
Softcover ISBN
978-3-642-64990-5
Series ISSN
0072-7830
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