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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Peak set without peak points


Author: Krzysztof Jarosz
Journal: Proc. Amer. Math. Soc. 125 (1997), 1377-1379
MSC (1991): Primary 46J10
MathSciNet review: 1372032
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Abstract: We give an example of a natural Banach function algebra on the unit disc such that a smaller disc is a peak set for the algebra, but it does not contain any peak point.


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

  • 1. H. G. Dales, Boundaries and peak points for Banach function algebras, Proc. London Math. Soc. (3) 22 (1971), 121–136. MR 0276770 (43 #2510)
  • 2. Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1969. MR 0410387 (53 #14137)
  • 3. T. G. Honary. An example of a Banach function algebra having a peak set without any peak point. In Proceedings of The Fifth Analysis Seminar at Shiraz University, pages 26-32, 1990.

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Additional Information

Krzysztof Jarosz
Affiliation: Department of Mathematics, Bowling Green State University, Bowling Green, Ohio 43403
Address at time of publication: Department of Mathematics & Statistics, Southern Illinois University, Edwardsville, Illinois 62026
Email: kjarosz@siue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03767-2
PII: S 0002-9939(97)03767-2
Received by editor(s): November 8, 1995
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1997 American Mathematical Society