Contribution to the classification of minimal extensions (Q1879763)
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scientific article; zbMATH DE number 2102583
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Contribution to the classification of minimal extensions |
scientific article; zbMATH DE number 2102583 |
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Contribution to the classification of minimal extensions (English)
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23 September 2004
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Some minimal extensions of \(\ell_1\) are studied. It is shown that some certain quasi-Banach spaces arising from quasi-linear functions on~\(\ell_1\) are not isomorphic: in particular, it is proved that \textit{M. Ribe's} space [Proc. Am. Math. Soc. 73, 351--355 (1979; Zbl 0397.46002)] contains no isomorphic copy of that of \textit{N. J. Kalton} [Compos. Math. 37, 243--276 (1978; Zbl 0395.46003)]. Also, a continuum of mutually non-isomorphic (Ribe like) minimal extensions of~\(\ell_1\) is constructed.
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minimal extension
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Banach space
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quasi-Banach space
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0.8839329
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0.8791328
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0.8722624
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0.87206316
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0.8715673
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0.8708192
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