Banach Algebras and Several Complex Variables

  • John Wermer

Part of the Graduate Texts in Mathematics book series (GTM, volume 35)

Table of contents

  1. Front Matter
    Pages i-ix
  2. John Wermer
    Pages 1-4
  3. John Wermer
    Pages 5-16
  4. John Wermer
    Pages 17-22
  5. John Wermer
    Pages 23-26
  6. John Wermer
    Pages 27-30
  7. John Wermer
    Pages 36-42
  8. John Wermer
    Pages 50-56
  9. John Wermer
    Pages 57-63
  10. John Wermer
    Pages 64-70
  11. John Wermer
    Pages 71-76
  12. John Wermer
    Pages 77-81
  13. John Wermer
    Pages 82-86
  14. John Wermer
    Pages 111-121
  15. John Wermer
    Pages 122-130
  16. John Wermer
    Pages 131-136

About this book

Introduction

During the past twenty years many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras. On the one hand, function theory has been used to answer algebraic questions such as the question of the existence of idempotents in a Banach algebra. On the other hand, concepts arising from the study of Banach algebras such as the maximal ideal space, the Silov boundary, Gleason parts, etc. have led to new questions and to new methods of proof in function theory. Roughly one third of this book isconcerned with developing some of the principal applications of function theory in several complex variables to Banach algebras. We presuppose no knowledge of severalcomplex variables on the part of the reader but develop the necessary material from scratch. The remainder of the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. For n > I no complete theory exists but many important particular problems have been solved. Throughout, our aim has been to make the exposition elementary and self-contained. We have cheerfully sacrificed generality and completeness all along the way in order to make it easier to understand the main ideas.

Keywords

Banach Banach algebra Banachsche Algebra Funktionentheorie Maxima Scratch Silo Variables algebra analytic function boundary element method cohomology function functions manifold

Authors and affiliations

  • John Wermer
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3878-0
  • Copyright Information Springer-Verlag New York 1976
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-3880-3
  • Online ISBN 978-1-4757-3878-0
  • Series Print ISSN 0072-5285
  • About this book