The lattice-isometric copies of \(\ell_{\infty}(\Gamma)\) in quotients of Banach lattices (Q1415151)
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scientific article; zbMATH DE number 2012591
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The lattice-isometric copies of \(\ell_{\infty}(\Gamma)\) in quotients of Banach lattices |
scientific article; zbMATH DE number 2012591 |
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The lattice-isometric copies of \(\ell_{\infty}(\Gamma)\) in quotients of Banach lattices (English)
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3 December 2003
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Summary: Let \(E\) be a Banach lattice and let \(M\) be a norm-closed and Dedekind \(\sigma\)-complete ideal of \(E\). If \(E\) contains a lattice-isometric copy of \(\ell_{\infty}\), then \(E/M\) contains such a copy as well, or \(M\) contains a lattice copy of \(\ell_{\infty}\). This is one of the consequences of more general results presented in this paper.
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Banach lattice
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lattice copy of \(\ell_\infty\)
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