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Keywords:
compact Hausdorff space $X$; the sup-norm algebra $C(X)$ of all complex-valued continuous functions on $X$; its closed subalgebras (called function algebras); measure orthogonal to a function algebra
compact Hausdorff space $X$; the sup-norm algebra $C(X)$ of all complex-valued continuous functions on $X$; its closed subalgebras (called function algebras); measure orthogonal to a function algebra
Summary:
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 $E$.
References:
[1] Bear, H. S.: Complex function algebras. Trans. Amer. Math. Soc. 90 (1959), 383–393. MR 0107164 | Zbl 0086.31602
[2] Hoffman, K., Singer, I. M.: Maximal algebras of continuous functions. Acta Math. 103 (1960), 217–241. MR 0117540
[3] Čerych, J.: On essential sets of function algebras in terms of their orthogonal measures. Comment. Math. Univ. Carolin. 36, 3 (1995), 471–474. MR 1364487
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