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A uniform algebra A on a compact Hausdorff topological space X is a closed (with respect to the uniform norm) subalgebra of the C*-algebra C(X) (the continuous complex valued functions on X) with the following properties: the constant functions are contained in Afor every x, y X there is fA with f(x)f(y). This is called separating the points of X. As a closed subalgebra of the commutative Banach algebra C(X) a uniform algebra is itself a unital commutative Banach algebra (when equipped with the uniform norm). Hence, it is, (by definition) a Banach function algebra.

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  • A uniform algebra A on a compact Hausdorff topological space X is a closed (with respect to the uniform norm) subalgebra of the C*-algebra C(X) (the continuous complex valued functions on X) with the following properties: the constant functions are contained in Afor every x, y X there is fA with f(x)f(y). This is called separating the points of X. As a closed subalgebra of the commutative Banach algebra C(X) a uniform algebra is itself a unital commutative Banach algebra (when equipped with the uniform norm). Hence, it is, (by definition) a Banach function algebra.
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  • Uniform algebra
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  • A uniform algebra A on a compact Hausdorff topological space X is a closed (with respect to the uniform norm) subalgebra of the C*-algebra C(X) (the continuous complex valued functions on X) with the following properties: the constant functions are contained in Afor every x, y X there is fA with f(x)f(y). This is called separating the points of X. As a closed subalgebra of the commutative Banach algebra C(X) a uniform algebra is itself a unital commutative Banach algebra (when equipped with the uniform norm). Hence, it is, (by definition) a Banach function algebra. A uniform algebra A on X is said to be natural if the maximal ideals of A precisely are the ideals of functions vanishing at a point x in X.
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