A nonclosed ideal that is not A nonclosed ideal that is not self-adjoint in a commutative C*-algebra.

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Consider C*-algebra A = C(D) and the ideal I = fA = {fg ; g Î A}, where f(z) = z. f*(z) = [`z] and if f* Î I, then there exists an element g Î A such that f* = fg. So g(0) = limz® 0g(z) = limz® 0[( [`z])/ z], a contradiction. Thus I isn't self-adjoint.

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On 22 Feb 2001, 00:18.