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Banach Algebras and Several Complex Variables

  • Textbook
  • © 1976

Overview

Authors:
  1. John Wermer

    1. Department of Mathematics, Brown University, Providence, USA

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

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Table of contents (22 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Preliminaries and Notations

    • John Wermer
    Pages 1-4

  3. Classical Approximation Theorems

    • John Wermer
    Pages 5-16

  4. Operational Calculus in One Variable

    • John Wermer
    Pages 17-22

  5. Differential Forms

    • John Wermer
    Pages 23-26

  6. The \(\overline \partial \)-Operator

    • John Wermer
    Pages 27-30

  7. The Equation \(\overline \partial \)u = ƒ

    • John Wermer
    Pages 31-35

  8. The Oka—Weil Theorem

    • John Wermer
    Pages 36-42

  9. Operational Calculus in Several Variables

    • John Wermer
    Pages 43-49

  10. The Šilov Boundary

    • John Wermer
    Pages 50-56

  11. Maximality and Radó’s Theorem

    • John Wermer
    Pages 57-63

  12. Analytic Structure

    • John Wermer
    Pages 64-70

  13. Algebras of Analytic Functions

    • John Wermer
    Pages 71-76

  14. Approximation on Curves in Cn

    • John Wermer
    Pages 77-81

  15. Uniform Approximation on Disks in Cn

    • John Wermer
    Pages 82-86

  16. The First Cohomology Group of a Maximal Ideal Space

    • John Wermer
    Pages 87-95

  17. The \(\overline \partial \)-Operator in Smoothly Bounded Domains

    • John Wermer
    Pages 96-110

  18. Manifolds Without Complex Tangents

    • John Wermer
    Pages 111-121

  19. Submanifolds of High Dimension

    • John Wermer
    Pages 122-130

  20. Generators

    • John Wermer
    Pages 131-136
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Brown University, Providence, USA

    John Wermer

Bibliographic Information

  • Book Title: Banach Algebras and Several Complex Variables

  • Authors: John Wermer

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-3878-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1976

  • eBook ISBN: 978-1-4757-3878-0Published: 29 June 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: IX, 161

  • Additional Information: Originally published by Markham

  • Topics: Algebra

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