The Banach-Mazur distance between \(C(\Delta)\) and \(C_0 (\Delta)\) equals \(2\) (Q6545462)
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scientific article; zbMATH DE number 7854994
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Banach-Mazur distance between \(C(\Delta)\) and \(C_0 (\Delta)\) equals \(2\) |
scientific article; zbMATH DE number 7854994 |
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The Banach-Mazur distance between \(C(\Delta)\) and \(C_0 (\Delta)\) equals \(2\) (English)
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29 May 2024
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Denote by \(C(\Delta)\) the Banach space of all continuous real-valued functions on the Cantor set \(\Delta\) and put \(C_{0}(\Delta)= \{f \in C(\Delta): f(1)=0 \}\). In this paper, it is proven that the Banach-Mazur distance between \(C(\Delta)\) and \(C_{0}(\Delta)\) is~$ 2$. As an immediate consequence, the authors solve a problem left open in [\textit{L.~Candido} and \textit{E.~M. Galego}, Fundam. Math. 218, No.~2, 151--163 (2012; Zbl 1258.46002)].
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Banach-Mazur distance
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Cantor set
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space of continuous functions
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