Additive Subgroups of Topological Vector Spaces

  • Authors
  • Wojciech Banaszczyk
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1466)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Wojciech Banaszczyk
    Pages 1-44
  3. Wojciech Banaszczyk
    Pages 45-71
  4. Wojciech Banaszczyk
    Pages 72-109
  5. Wojciech Banaszczyk
    Pages 110-131
  6. Wojciech Banaszczyk
    Pages 132-167
  7. Back Matter
    Pages 168-178

About this book

Introduction

The Pontryagin-van Kampen duality theorem and the Bochner theorem on positive-definite functions are known to be true for certain abelian topological groups that are not locally compact. The book sets out to present in a systematic way the existing material. It is based on the original notion of a nuclear group, which includes LCA groups and nuclear locally convex spaces together with their additive subgroups, quotient groups and products. For (metrizable, complete) nuclear groups one obtains analogues of the Pontryagin duality theorem, of the Bochner theorem and of the Lévy-Steinitz theorem on rearrangement of series (an answer to an old question of S. Ulam). The book is written in the language of functional analysis. The methods used are taken mainly from geometry of numbers, geometry of Banach spaces and topological algebra. The reader is expected only to know the basics of functional analysis and abstract harmonic analysis.

Keywords

Abstract harmonic analysis Banasche Algebra Kombinatorik Vector space combinatorics functional analysis geometry of Banach spaces geometry of numbers topological groups

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0089147
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-53917-9
  • Online ISBN 978-3-540-46396-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book