In my research in operator theory, specifically in C* algebras and enveloping, I came across this strange footnote in a text (locally published in non English where I study) which states the following:

Suppose we have X a compact topological space, now suppose we have A, a sub-algebra of the algebra of continuous functions $ C(X) $ and we know A contains 1 (the identity) and that A separates points, in this case we know A is an operator algebra, and we also know the C*-enveloping $ C_{e}^{*}(A) $ is commutative and that there exists a topological space F such that $ C_{e}^{*}(A) \simeq C(F) $.

OK, I'll admit I am not an expert on enveloping of C* algebras, but this seems really strange to me non the less as it is said as if it is an elementary result but still it is beyond my reach, why is $ C_{e}^{*}(A) $ necessarily commutative and why do we must have $ C_{e}^{*}(A) \simeq C(F) $, I do not even know what the topological space F is nor do I have any idea how to begin to construct it. Can someone please help me by explaining this strange remark I came across? It seems like valuable information to know but I cannot find it anywhere or understand it. I thank all helpers.

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