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Generators

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

Abstract

Let 𝔄 be a uniform algebra on a compact space X. Fix f 1,..., f k ∈ 𝔄 and denote, as earlier, by
$$\left[ {{f_{1,...}}{f_{k\backslash }}|X} \right]$$
the smallest closed subalgebra of 𝔄 which contains the constants and f 1,..., f k. If [f 1,..., f k |X] = 𝔄, we say the f j are a set of generators for 𝔄. In earlier sections we obtained criteria for a set f 1, ..., f k to be a set of generators for the algebra C(X). Here we shall study the case when 𝔄 = A(D) the disk algebra, and more generally the case 𝔄 = A(B) where B is the closed ball in C n
$${\left| {{z_1}} \right|^2} + ... + {\left| {{z_n}} \right|^2} \le 1$$
and A(B) consists of all functions continuous in B and analytic in .

Keywords

Singular Point Closed Unit Ball Uniform Algebra Analytic Disk Maximal Ideal Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1976

Authors and Affiliations

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

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