On Rosenthal's \(\ell^ 1\)-theorem (Q1323131)
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scientific article; zbMATH DE number 566518
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Rosenthal's \(\ell^ 1\)-theorem |
scientific article; zbMATH DE number 566518 |
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On Rosenthal's \(\ell^ 1\)-theorem (English)
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9 May 1994
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Rosenthal's \(\ell^ 1\)-theorem can be restated by saying that a bounded sequence \((x_ n)\) in a Banach space admits a subsequence which is weakly Cauchy provided that there are ``many'' arbitrarily small \(\ell^ 1\)-blocks of the \(x_ n\). Here we show that there is even a norm convergent subsequence if these blocks can be chosen such that their length is bounded.
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Rosenthal's \(\ell^ 1\)-theorem
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small \(\ell^ 1\)-blocks
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