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

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Merino-Cruz H., Wawrzyńczyk A.

Commentationes Mathematicae

2014

tom 54

nr 1

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

Ograniczanie wyników

1 Commentationes Mathematicae

1 Merino-Cruz H.

1 Wawrzyńczyk A.

1 2014

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