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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 | References | Similar Articles | Additional Information

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. Lennart Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. of Math. (2) 76 (1962), 547–559. MR 0141789
  • 2. T. W. Gamelin, Uniform algebras and Jensen measures, London Mathematical Society Lecture Note Series, vol. 32, Cambridge University Press, Cambridge-New York, 1978. MR 521440
  • 3. Nessim Sibony, Un exemple de domaine pseudoconvexe régulier où l’équation ∂𝑢=𝑓 n’admet pas de solution bornée pour 𝑓 bornée, Invent. Math. 62 (1980/81), no. 2, 235–242 (French). MR 595587, 10.1007/BF01389159

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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.