A note on the Banach-Steinhaus theorem (Q1189101)
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scientific article; zbMATH DE number 54518
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the Banach-Steinhaus theorem |
scientific article; zbMATH DE number 54518 |
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A note on the Banach-Steinhaus theorem (English)
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26 September 1992
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Let \((T_ i)\) be a family of bounded linear operators between Banach spaces such that \(\sup | T_ i|=\infty\). By the Banach-Steinhaus theorem, the set \(E=\{x:\) \(\sup | T_ i x|<\infty\}\) is `thin', namely a countable union of nowhere dense sets. Here it is shown that \(E\) is also thin in a different sense: it is a countable union of so-called porous sets.
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open mapping theorem
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thin
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family of bounded linear operators between Banach spaces
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Banach-Steinhaus theorem
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countable union of nowhere dense sets
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countable union of porous sets
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