In the present note, we characterize the essential set $E$ of a function algebra $A$ defined on a compact Hausdorff space $X$ in terms of local properties of functions in $A$ at the points off $E$.
@article{107905,
author = {Jan \v Cerych},
title = {A characterization of essential sets of function algebras},
journal = {Archivum Mathematicum},
volume = {040},
year = {2004},
pages = {229-232},
zbl = {1115.46041},
mrnumber = {2107017},
language = {en},
url = {http://dml.mathdoc.fr/item/107905}
}
Čerych, Jan. A characterization of essential sets of function algebras. Archivum Mathematicum, Tome 040 (2004) pp. 229-232. http://gdmltest.u-ga.fr/item/107905/
Complex function algebras, Trans. Amer. Math. Soc. 90 (1959), 383–393. | MR 0107164 | Zbl 0086.31602
Maximal algebras of continuous functions, Acta Math. 103 (1960), 217–241. | MR 0117540
On essential sets of function algebras in terms of their orthogonal measures, Comment. Math. Univ. Carolin. 36, 3 (1995), 471–474. | MR 1364487