Uniform Algebra
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 A for every x, y in X there is finA with f(x)nef(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 Bana...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 A for every x, y in X there is finA with f(x)nef(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 Mx of functions vanishing at a point x in X.
