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Closed ideals of \(A^ +\) and the Cantor set. (English) Zbl 0791.46027
Let \(A^ +\) be the algebra of analytic functions in the disc whose series of Taylor coefficients at the origin is absolutely convergent. Closed ideals of \(A^ +\) whose hull is finite or countable were characterized by Kahane and Bennett-Gilbert, and it was conjectured that any closed ideal \(I\) of \(A^ +\) has the form \(S_ I H^ \infty\cap I^ A\) where \(I^ A\) is the closed ideal \(I\) of the Wiener algebra \(A(\Gamma)\) generated by \(I\) and where \(S_ I\) is the greatest common divisor of the inner factors of the nonzero elements of \(I\). The results of this paper show that this conjecture is true when \(h(I)\cap\Gamma\), the intersection of the hull of \(I\) with the unit circle \(\Gamma\), is contained in the triadic Cantor set.

MSC:
46J20 Ideals, maximal ideals, boundaries
30H05 Spaces of bounded analytic functions of one complex variable
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