© 1971

Topological Vector Spaces


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

Table of contents

  1. Front Matter
    Pages I-11
  2. Helmut H. Schaefer
    Pages 12-35
  3. Helmut H. Schaefer
    Pages 36-72
  4. Helmut H. Schaefer
    Pages 73-121
  5. Helmut H. Schaefer
    Pages 122-202
  6. Helmut H. Schaefer
    Pages 203-257
  7. Back Matter
    Pages 258-296

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 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.


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Authors and affiliations

  1. 1.University of TübingenGermany

Bibliographic information

  • Book Title Topological Vector Spaces
  • Authors H.H. Schaefer
  • Series Title Graduate Texts in Mathematics
  • DOI
  • Copyright Information Springer-Verlag New York 1971
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-90026-1
  • Softcover ISBN 978-0-387-05380-6
  • eBook ISBN 978-1-4684-9928-5
  • Series ISSN 0072-5285
  • Edition Number 1
  • Number of Pages XI, 296
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published by Macmillan Company 1967
  • Topics Mathematics, general
  • Buy this book on publisher's site
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