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

Merino-Cruz H., Wawrzyńczyk A.

Commentationes Mathematicae

2014

Vol 54, No. 1

29--37

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 A1(D) nowhere vanishing in D we associate a Banach algebra AnG(D) contained in the disc algebra A(D). We prove that all closed ideals of AnG(D) of at most countable hull are of the standard form.