On the complexity of Hamel bases of infinite-dimensional Banach spaces (Q2717746)
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scientific article; zbMATH DE number 1605334
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the complexity of Hamel bases of infinite-dimensional Banach spaces |
scientific article; zbMATH DE number 1605334 |
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On the complexity of Hamel bases of infinite-dimensional Banach spaces (English)
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17 June 2001
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Baire property
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Banach space
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Borel set
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Hamel basis
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Baire category
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0.9025738
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0.8971404
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0.88403076
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0.8743906
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0.87428606
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Using a Baire category argument, it is shown that if \(H\) is a Hamel basis of an infinite-dimensional Banach space \(X\), then there is an \(N\geq 1\) such that the set of all linear combinations of \(N\) elements of the basis, with non-zero coefficients, is not a Borel subset of \(X\). This answers a question of A. Plichko. Note an obvious misprint at the last line of page 133: \(B\) should be replaced by \(X\).
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