# zbMATH — the first resource for mathematics

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 $$\overline I_G$$.

##### MSC:
 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
Full Text: