A note on multiplier algebras on reproducing kernel Hilbert spaces
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- by Tavan T. Trent PDF
- Proc. Amer. Math. Soc. 136 (2008), 2835-2838 Request permission
Abstract:
We construct a simple reproducing kernel space whose multiplier algebra does not satisfy a “corona theorem”.References
- Lennart Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. of Math. (2) 76 (1962), 547–559. MR 141789, DOI 10.2307/1970375
- 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
- Nessim Sibony, Un exemple de domaine pseudoconvexe régulier où l’équation $\bar \partial u=f$ n’admet pas de solution bornée pour $f$ bornée, Invent. Math. 62 (1980/81), no. 2, 235–242 (French). MR 595587, DOI 10.1007/BF01389159
Additional Information
- Tavan T. Trent
- Affiliation: Department of Mathematics, The University of Alabama, Box 870350, Tuscaloosa, Alabama 35487-0350
- Email: ttrent@as.ua.edu
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2835-2838
- MSC (2000): Primary 46E22, 47B32
- DOI: https://doi.org/10.1090/S0002-9939-08-09383-0
- MathSciNet review: 2399048