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Uniform algebra

In functional analysis, 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 X there is fA with f(x)f(y). This is called separating the points of X.

Abstract characterization
If A is a unital commutative Banach algebra such that ||a^2|| = ||a||^2 for all a in A, then there is a compact Hausdorff X such that A is isomorphic as a Banach algebra to a uniform algebra on X. This result follows from the spectral radius formula and the Gelfand representation. == Notes ==
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