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On closed ideals in a certain class of algebras of holomorphic functions. (English) Zbl 1329.30027
This paper is a continuation of the authors’ work in [Commentat. Math. 54, No. 1, 29–37 (2014; Zbl 1328.46040)]. It is shown that in specific subalgebras of the disk algebra of type \(A^G_n\) certain closed ideals are standard. The results are motivated by Korenblum’s characterization of the closed ideals in \(A^n(\mathbb D)\) [B. I. Korenbljum, Funct. Anal. Appl. 6, 203–214 (1973; Zbl 0262.46053); translation from Funkts. Anal. Prilozh. 6, No. 3, 38–52 (1972)]. In the final section the authors construct, under suitable conditions on \(G\in A^n(\mathbb D)\), approximate units for the ideals \(\overline I_G\).

30H50 Algebras of analytic functions of one complex variable
46J20 Ideals, maximal ideals, boundaries
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
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