On the barrelledness of \(\ell^ p\)-direct sums of seminormed spaces for \(1\leq p\leq \infty\) (Q1322611)
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scientific article; zbMATH DE number 563369
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the barrelledness of \(\ell^ p\)-direct sums of seminormed spaces for \(1\leq p\leq \infty\) |
scientific article; zbMATH DE number 563369 |
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On the barrelledness of \(\ell^ p\)-direct sums of seminormed spaces for \(1\leq p\leq \infty\) (English)
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21 August 1994
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Let \((X_ i)_{i\in I}\) be a family of seminormed spaces. It is proved that the \(\ell^ p\)-direct sum of the spaces \(X_ i\) \((1\leq p\leq \infty)\) is barrelled (ultrabarrelled) or semi-Baire-like iff every \(X_ i\) is barrelled (ultrabarrelled) or semi-Baire-like, respectively. This extends a result of P. Lurje.
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ultrabarrelled
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seminormed spaces
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\(\ell^ p\)-direct sum
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semi-Baire- like
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barrelled
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