Relations between Banach function algebras and their uniform closures
Author: Taher G. Honary
Journal: Proc. Amer. Math. Soc. 109 (1990), 337-342
MSC: Primary 46J20; Secondary 46J10
MathSciNet review: 1007499
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Abstract: Let $A$ be a Banach function algebra on a compact Hausdorff space $X$. In this paper we consider some relations between the maximal ideal space, the Shilov boundary and the Choquet boundary of $A$ and its uniform closure $\bar A$. As an application we determine the maximal ideal space, the Shilov boundary and the Choquet boundary of algebras of infinitely differentiable functions which were introduced by Dales and Davie in 1973.
- H. G. Dales and A. M. Davie, Quasianalytic Banach function algebras, J. Functional Analysis 13 (1973), 28–50. MR 0343038, DOI https://doi.org/10.1016/0022-1236%2873%2990065-7
- Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1969. MR 0410387
- Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101
H. G. Dales and A. M. Davie, Quasianalytic Banach function algebras, J. Funct. Anal. (1) 13 (1973), 28-50.
T. W. Gamelin, Uniform algebras, Prentice-Hall, Englewood Cliffs, NJ, 1969.
C. E. Rickart, General theory of Banach algebras, Van Nostrand, Princeton, NJ, 1960.
Keywords: Banach function algebras, uniform algebras, maximal ideal space, Shilov boundary, Banach algebras of differentiable functions
Article copyright: © Copyright 1990 American Mathematical Society