Locally Convex Spaces

  • M. Scott Osborne

Part of the Graduate Texts in Mathematics book series (GTM, volume 269)

Table of contents

  1. Front Matter
    Pages i-viii
  2. M. Scott Osborne
    Pages 1-32
  3. M. Scott Osborne
    Pages 33-49
  4. M. Scott Osborne
    Pages 51-94
  5. M. Scott Osborne
    Pages 95-121
  6. M. Scott Osborne
    Pages 123-163
  7. M. Scott Osborne
    Pages 165-174
  8. Back Matter
    Pages 175-213

About this book


For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convex topological vector spaces, is intended to cover most of the general theory needed for application to other areas of analysis.  Normed vector spaces, Banach spaces, and Hilbert spaces are all examples of classes of locally convex spaces, which is why this is an important topic in functional analysis.

While this graduate text focuses on what is needed for applications, it also shows the beauty of the subject and motivates the reader with exercises of varying difficulty. Key topics covered include point set topology, topological vector spaces, the Hahn–Banach theorem, seminorms and Fréchet spaces, uniform boundedness, and dual spaces. The prerequisite for this text is the Banach space theory typically taught in a beginning graduate real analysis course.


Fredholm theory Fréchet Spaces Hahn–Banach Theorem Montel spaces dual spaces locally convex spaces topological groups

Authors and affiliations

  • M. Scott Osborne
    • 1
  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-02044-0
  • Online ISBN 978-3-319-02045-7
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • Buy this book on publisher's site