The density of peak points in the Shilov boundary of a Banach function algebra
Abstract: H. G. Dales has proved in  that if is a Banach function algebra on a compact metrizable space , then , where is the set of peak points of (w.r.t. ) and is the Shilov boundary of (w.r.t. ). Here, by considering the relation between peak sets and peak points of a Banach function algebra and its uniform closure , we present an elementary and constructive proof of the density of peak points in the Shilov boundary.
-  H. G. Dales, Boundaries and peak points for Banach function algebras, Proc. London Math. Soc. (3) 22 (1971), 121–136. MR 0276770, https://doi.org/10.1112/plms/s3-22.1.121
-  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
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