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


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 .


Singular Point Closed Unit Ball Uniform Algebra Analytic Disk Maximal Ideal Space 
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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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