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A note on multiplier algebras on reproducing kernel Hilbert spaces

Author(s): Tavan T. Trent
Journal: Proc. Amer. Math. Soc. 136 (2008), 2835-2838.
MSC (2000): Primary 46E22, 47B32
Posted: March 28, 2008
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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:

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 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
Email: ttrent@as.ua.edu

DOI: 10.1090/S0002-9939-08-09383-0
PII: S 0002-9939(08)09383-0
Keywords: Corona, reproducing kernel
Received by editor(s): February 8, 2007
Posted: March 28, 2008
Additional Notes: The author was partially supported by NSF Grant DMS-0400307
Communicated by: Michael T. Lacey
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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