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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; pervasive (analytic; integrity domain; antisymmetric) function algebra; 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; pervasive (analytic; integrity domain; antisymmetric) function algebra; measure orthogonal to a function algebra
Summary:
In the present note, we characterize the pervasive, analytic, integrity domain and the antisymmetric function algebras respectively, defined on a compact Hausdorff space $X$, in terms of their orthogonal measures on $X$.
References:
[1] Helson H., Quigley F.: Maximal algebras of continuous functions. Proc. Amer. Math. Soc. 8 (1957), 111-114. MR 0084732 | Zbl 0078.29004
[2] Hoffman K., Singer I.M.: Maximal algebras of continuous functions. Acta Math. 103 (1960), 217-241. MR 0117540 | Zbl 0195.13903
[3] Čerych J.: A word on pervasive function spaces. Conference. Complex Analysis and Applications '80, Sofia, 1984, pp. 107-109. MR 0883224
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