Copies of \(\ell_\infty\) in Köthe spaces of vector valued functions (Q811657)
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scientific article; zbMATH DE number 4216407
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Copies of \(\ell_\infty\) in Köthe spaces of vector valued functions |
scientific article; zbMATH DE number 4216407 |
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Copies of \(\ell_\infty\) in Köthe spaces of vector valued functions (English)
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1992
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It is shown that \(\ell_ \infty\) embeds into a Köthe space \(E(X)\) of vector valued functions if and only if it embeds into either \(E\) or \(X\). This result is obtained embedding ``locally'' \(E(X)\) into a suitable space of Bochner integrable functions and then using a recent result due to Mendoza about the existence of copies of \(\ell_ \infty\) inside \(L^ 1(X)\).
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Köthe space of vector valued functions
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space of Bochner integrable functions
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