Ukrainian Mathematical Journal

, Volume 42, Issue 5, pp 546–549 | Cite as

Generalized analytic functions and analytic subalgebras

  • O. V. Ivanov
Article

Abstract

Two-sheeted analogues of the corona theorem are given for algebras of arbitrary bounded continuous functions in the open disk with angular boundary values from analytic subalgebras
. The fundamental result is the description of the structure of the space of the maximal ideals of such algebras in the case of an arbitrary analytic subalgebra
.

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Literature cited

  1. 1.
    J. B. Garnett, Bounded Analytic Functions, Academic Press, New York (1981).Google Scholar
  2. 2.
    K. Izuchi and Y. Izuchi, “Algebras of bounded analytic functions containing the disk algebra,” Can. J. Math.,38, No. 1, 87–108 (1986).Google Scholar
  3. 3.
    O. V. Ivanov, “Generalized analytic functions and the two-sheeted corona theorem,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 5, 10–11 (1989).Google Scholar
  4. 4.
    V. A. Tolokonnikov, The corona theorem in algebras of bounded analytic functions. Manuscript deposited at VINITI, No. 251–84 Dep. (1984).Google Scholar
  5. 5.
    S. Y. A. Chang, “Some algebras of bounded analytic functions containing the disk algebra,” Lecture Notes in Math., No. 604, 12–20 (1977).Google Scholar
  6. 6.
    C. Sundberg and T. H. Wolff, “Interpolating sequences for QAB,” Trans. Am, Math. Soc.,276, No. 2, 551–581 (1983).Google Scholar
  7. 7.
    T. W. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs (1969).Google Scholar
  8. 8.
    O. V. Ivanov, “Generalized Douglas algebras and the corona theorem,” Sib. Mat. Zh.,31, No. 4, 60–65 (1990).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • O. V. Ivanov
    • 1
  1. 1.Institute for Applied Mathematics and MechanicsAcademy of Sciences of the Ukrainian SSRDonetsk

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