A note on the intersection of Banach subspaces (Q1884450)
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scientific article; zbMATH DE number 2113000
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the intersection of Banach subspaces |
scientific article; zbMATH DE number 2113000 |
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A note on the intersection of Banach subspaces (English)
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1 November 2004
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In this article, the authors prove that a Banach space \(X\) is reflexive if and only if, for every \(x \in X\) and every decreasing sequence \((X_n)\) of closed subspaces of \(X\), \(d(x,\bigcap_{n=1}^\infty X_n) = \lim_{n\to\infty} d(x,X_n)\) where \(d(x,C)\) denotes the distance from \(x\) to \(C\).
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reflexive
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Banach space
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