© 1973

Complete Normed Algebras


Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 80)

Table of contents

  1. Front Matter
    Pages I-X
  2. Frank F. Bonsall, John Duncan
    Pages 1-74
  3. Frank F. Bonsall, John Duncan
    Pages 75-118
  4. Frank F. Bonsall, John Duncan
    Pages 119-153
  5. Frank F. Bonsall, John Duncan
    Pages 154-186
  6. Frank F. Bonsall, John Duncan
    Pages 187-229
  7. Frank F. Bonsall, John Duncan
    Pages 230-250
  8. Frank F. Bonsall, John Duncan
    Pages 251-273
  9. Back Matter
    Pages 274-304

About this book


The axioms of a complex Banach algebra were very happily chosen. They are simple enough to allow wide ranging fields of application, notably in harmonic analysis, operator theory and function algebras. At the same time they are tight enough to allow the development of a rich collection of results, mainly through the interplay of the elementary parts of the theories of analytic functions, rings, and Banach spaces. Many of the theorems are things of great beauty, simple in statement, surprising in content, and elegant in proof. We believe that some of them deserve to be known by every mathematician. The aim of this book is to give an account of the principal methods and results in the theory of Banach algebras, both commutative and non­ commutative. It has been necessary to apply certain exclusion principles in order to keep our task within bounds. Certain classes of concrete Banach algebras have a very rich literature, namely C*-algebras, function algebras, and group algebras. We have regarded these highly developed theories as falling outside our scope. We have not entirely avoided them, but have been concerned with their place in the general theory, and have stopped short of developing their special properties. For reasons of space and time we have omitted certain other topics which would quite naturally have been included, in particular the theories of multipliers and of extensions of Banach algebras, and the implications for Banach algebras of some of the standard algebraic conditions on rings.


Algebras Banach algebra Banachsche Algebra C*-algebra algebra analytic function

Authors and affiliations

  1. 1.Mathematical InstituteUniversity of EdinburghUK
  2. 2.Department of MathematicsUniversity of StirlingUK

Bibliographic information

  • Book Title Complete Normed Algebras
  • Authors Frank F. Bonsall
    John Duncan
  • Series Title Ergebnisse der Mathematik und ihrer Grenzgebiete
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1973
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-06386-5
  • Softcover ISBN 978-3-642-65671-2
  • eBook ISBN 978-3-642-65669-9
  • Series ISSN 0071-1136
  • Edition Number 1
  • Number of Pages X, 304
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Linear and Multilinear Algebras, Matrix Theory
    Operator Theory
    Functional Analysis
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