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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 of a function algebra defined on a compact Hausdorff space $X$ in terms of its orthogonal measures on $X$.
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 | Zbl 0195.13903
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