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A note on multiplier algebras on reproducing kernel Hilbert spaces

Author: Tavan T. Trent
Journal: Proc. Amer. Math. Soc. 136 (2008), 2835-2838
MSC (2000): Primary 46E22, 47B32
Published electronically: March 28, 2008
MathSciNet review: 2399048
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Abstract: We construct a simple reproducing kernel space whose multiplier algebra does not satisfy a ``corona theorem''.

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

  • 1. L. Carleson, Interpolation by bounded analytic functions and the corona problem, Annals of Math. 76 (1962), 547-559. MR 0141789 (25:5186)
  • 2. T. W. Gamelin, Uniform Algebras and Jensen Measures, London Mathematical Society Lecture Note Series 32, Cambridge University Press, Cambridge, 1978. MR 521440 (81a:46058)
  • 3. N. Sibony, Un exemple de domain pseudoconvexe régulier où l'équation $ \overline{\partial} u=f$ n'admet pas de solution bornée pour $ f$ bornée, Invent. Math. 62 (1980/81), 235-242. MR 595587 (82c:32020)

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Additional Information

Tavan T. Trent
Affiliation: Department of Mathematics, The University of Alabama, Box 870350, Tuscaloosa, Alabama 35487-0350

Keywords: Corona, reproducing kernel
Received by editor(s): February 8, 2007
Published electronically: March 28, 2008
Additional Notes: The author was partially supported by NSF Grant DMS-0400307
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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