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Compact Textbooks in Mathematics

A Course on Topological Vector Spaces

Authors: Voigt, Jürgen

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  • Includes a streamlined introduction to the duality theory of locally convex spaces, culminating in the Mackey-Arens theorem
  • Treats various important topics concerning the weak topology of Banach spaces
  • Discusses examples of function spaces which occur in applications to differential operators and measure theory
  • Provides as a highlight the treatment of weak compactness in L_1-spaces
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eBook 13,90 €
28,88 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-32945-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 18,71 €
36,39 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-32944-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

This book provides an introduction to the theory of topological vector spaces, with a focus on locally convex spaces. It discusses topologies in dual pairs, culminating in the Mackey-Arens theorem, and also examines the properties of the weak topology on Banach spaces, for instance Banach’s theorem on weak*-closed subspaces on the dual of a Banach space (alias the Krein-Smulian theorem), the Eberlein-Smulian theorem, Krein’s theorem on the closed convex hull of weakly compact sets in a Banach space, and the Dunford-Pettis theorem characterising weak compactness in L1-spaces. Lastly, it addresses topics such as the locally convex final topology, with the application to test functions D(Ω) and the space of distributions, and the Krein-Milman theorem. 

The book adopts an “economic” approach to interesting topics, and avoids exploring all the arising side topics. Written in a concise mathematical style, it is intended primarily for advanced graduate students with a background in elementary functional analysis, but is also useful as a reference text for established mathematicians. 

 


About the authors

Jürgen Voigt is Professor at the Institute of Analysis of the Technische Universität in Dresden, Germany.


Reviews

“The book may be highly recommended to all students and researchers with some knowledge of Banach or Hilbert space oriented functional analysis who want to learn its general abstract foundations.” (Jochen Wengenroth, zbMATH 1453.46001, 2021)


Table of contents (17 chapters)

Table of contents (17 chapters)
  • Initial Topology, Topological Vector Spaces, Weak Topology

    Pages 1-9

    Voigt, Jürgen

  • Convexity, Separation Theorems, Locally Convex Spaces

    Pages 11-21

    Voigt, Jürgen

  • Polars, Bipolar Theorem, Polar Topologies

    Pages 23-28

    Voigt, Jürgen

  • The Tikhonov and Alaoglu–Bourbaki Theorems

    Pages 29-35

    Voigt, Jürgen

  • The Mackey–Arens Theorem

    Pages 37-43

    Voigt, Jürgen

Buy this book

eBook 13,90 €
28,88 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-32945-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 18,71 €
36,39 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-32944-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
A Course on Topological Vector Spaces
Authors
Series Title
Compact Textbooks in Mathematics
Copyright
2020
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-32945-7
DOI
10.1007/978-3-030-32945-7
Softcover ISBN
978-3-030-32944-0
Series ISSN
2296-4568
Edition Number
1
Number of Pages
VIII, 155
Number of Illustrations
1 illustrations in colour
Topics