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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Generators for $A(\Omega )$
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by N. Sibony and J. Wermer PDF
Trans. Amer. Math. Soc. 194 (1974), 103-114 Request permission


We consider a bounded domain $\Omega$ in ${{\mathbf {C}}^n}$ and the Banach algebra $A(\Omega )$ of all continuous functions on $\bar \Omega$ which are analytic in $\Omega$. Fix ${f_1}, \ldots ,{f_k}$ in $A(\Omega )$. We say they are a set of generators if $A(\Omega )$ is the smallest closed subalgebra containing the ${f_i}$. We restrict attention to the case when $\Omega$ is strictly pseudoconvex and smoothly bounded and the ${f_i}$ are smooth on $\bar \Omega$. In this case, Theorem 1 below gives conditions assuring that a given set ${f_i}$ is a set of generators.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 194 (1974), 103-114
  • MSC: Primary 32E25; Secondary 46J15
  • DOI:
  • MathSciNet review: 0419838