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A tetrachotomy for certain algebras containing the disc algebra


Author: Alexander J. Izzo
Journal: Proc. Amer. Math. Soc. 138 (2010), 623-627
MSC (2000): Primary 46J10, 46J15, 30H05
DOI: https://doi.org/10.1090/S0002-9939-09-10097-7
Published electronically: September 16, 2009
MathSciNet review: 2557179
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ D$ denote the open unit disc in the complex plane, and let $ A(D)$ denote the disc algebra. The algebras $ A(D)[f, \overline f ] \cap C(\overline D)$, where $ f$ is in $ H^\infty(D)$, are characterized. This answers a question raised by Joseph Cima.


References [Enhancements On Off] (What's this?)

  • 1. S. Axler and A. Shields, Algebras generated by analytic and harmonic functions, Indiana Univ. Math. J. 36 (1987), 631-638. MR 905614 (88h:46102)
  • 2. E. M. Čirka, Approximation by holomorphic functions on smooth manifolds in $ \mathbb{C}^n$, Mat. Sb. (N.S.) 78 (1969), 101-123; English transl., Math. USSR Sb. 7 (1969), 95-114. MR 0239121 (39:480)
  • 3. T. W. Gamelin, Uniform Algebras, 2nd ed., Chelsea, New York, 1984.
  • 4. J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981. MR 628971 (83g:30037)
  • 5. A. J. Izzo, Algebras containing bounded holomorphic functions, Indiana Univ. Math. J. 52 (2003), 1305-1342. MR 2010729 (2004h:46055)
  • 6. A. J. Izzo, Algebras generated by the disc algebra and bounded harmonic functions, Proc. Amer. Math. Soc. 135 (2007), 1065-1071. MR 2262907 (2007k:46087)
  • 7. W. Rudin, Real and Complex Analysis, 3rd ed., McGraw-Hill, New York, 1987. MR 924157 (88k:00002)

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Additional Information

Alexander J. Izzo
Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
Email: aizzo@math.bgsu.edu

DOI: https://doi.org/10.1090/S0002-9939-09-10097-7
Received by editor(s): May 4, 2009
Published electronically: September 16, 2009
Dedicated: Dedicated to the memory of Juha Heinonen
Communicated by: Mario Bonk
Article copyright: © Copyright 2009 American Mathematical Society

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