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Natural Function Algebras

  • Charles E. Rickart

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Charles E. Rickart
    Pages 1-13
  3. Charles E. Rickart
    Pages 14-30
  4. Charles E. Rickart
    Pages 31-43
  5. Charles E. Rickart
    Pages 44-56
  6. Charles E. Rickart
    Pages 57-72
  7. Charles E. Rickart
    Pages 73-94
  8. Charles E. Rickart
    Pages 95-107
  9. Charles E. Rickart
    Pages 108-123
  10. Charles E. Rickart
    Pages 124-135
  11. Charles E. Rickart
    Pages 136-151
  12. Charles E. Rickart
    Pages 152-171
  13. Charles E. Rickart
    Pages 172-192
  14. Charles E. Rickart
    Pages 193-209
  15. Charles E. Rickart
    Pages 210-229
  16. Back Matter
    Pages 230-240

About this book

Introduction

The term "function algebra" usually refers to a uniformly closed algebra of complex valued continuous functions on a compact Hausdorff space. Such Banach alge­ bras, which are also called "uniform algebras", have been much studied during the past 15 or 20 years. Since the most important examples of uniform algebras consist of, or are built up from, analytic functions, it is not surprising that most of the work has been dominated by questions of analyticity in one form or another. In fact, the study of these special algebras and their generalizations accounts for the bulk of the re­ search on function algebras. We are concerned here, however, with another facet of the subject based on the observation that very general algebras of continuous func­ tions tend to exhibit certain properties that are strongly reminiscent of analyticity. Although there exist a variety of well-known properties of this kind that could be mentioned, in many ways the most striking is a local maximum modulus principle proved in 1960 by Hugo Rossi [RIl]. This result, one of the deepest and most elegant in the theory of function algebras, is an essential tool in the theory as we have developed it here. It holds for an arbitrary Banaeh algebra of £unctions defined on the spectrum (maximal ideal space) of the algebra. These are the algebras, along with appropriate generalizations to algebras defined on noncompact spaces, that we call "natural func­ tion algebras".

Keywords

Funktionenalgebra Lemma Natural Vector space algebra boundary element method eXist function functions integral maximum principle polynomial sets theorem topology

Authors and affiliations

  • Charles E. Rickart
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-8070-2
  • Copyright Information Springer-Verlag New York 1979
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90449-8
  • Online ISBN 978-1-4613-8070-2
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
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