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Peak set without peak points. (English) Zbl 0870.46032

Summary: 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.

MSC:

46J10 Banach algebras of continuous functions, function algebras
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References:

[1] H. G. Dales, Boundaries and peak points for Banach function algebras, Proc. London Math. Soc. (3) 22 (1971), 121 – 136. · Zbl 0211.15902 · doi:10.1112/plms/s3-22.1.121
[2] Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1969. · Zbl 0213.40401
[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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