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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 ''A'' : for every ''x'', ''y'' ''X'' there is f''A'' 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''. ==Abstract characterization== If ''A'' is a unital commutative Banach algebra such that 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「uniform algebra」の詳細全文を読む スポンサード リンク
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