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Closed ideals in a new class of algebras of holomorphic functions on the disc

Hector Merino-Cruz; Antoni Wawrzyńczyk — 2014

Commentationes Mathematicae

We define a new class of Banach algebras of holomorphic functions on the unit disc $𝔻$ which contains the algebras studied in [GMR2] and [GW]. To a function G of the class $𝒜^{1} (𝔻)$ nowhere vanishing in $𝔻$ we associate a Banach algebra $𝒜_{G}^{n} (𝔻)$ contained in the disc algebra $𝒜 (𝔻)$ . We prove that all closed ideals of $𝒜_{G}^{n} (𝔻)$ of at most countable hull are of the standard form.

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