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\(A^p\) is not an algebra for \(1 < p < 2\). (English) Zbl 1333.46050

Summary: Let \(A^p\) be the Banach space of all continuous functions on the torus \(\mathbb{T} = \{ z \in \mathbb{C} || z | = 1 \}\) whose Fourier coefficients are in \(\ell^p\). We show that \(A^p\) is not an algebra for all \(1 < p < 2\).

MSC:

46J10 Banach algebras of continuous functions, function algebras
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Full Text: Euclid