On subspaces isomorphic to \(\ell^q\) in interpolation of quasi Banach spaces (Q2704060)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On subspaces isomorphic to \(\ell^q\) in interpolation of quasi Banach spaces |
scientific article |
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13 May 2001
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existence of isomorphic copies of \(\ell_q\)
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interpolation Banach spaces
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quasi-Banach spaces
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On subspaces isomorphic to \(\ell^q\) in interpolation of quasi Banach spaces (English)
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The following extension of a result of \textit{M. Lévy} [C. R. Acad. Sci. Paris, Sér. A 289, 675-677 (1979; Zbl 0421.46028)] about the existence of isomorphic copies of \(\ell_q\) in interpolation Banach spaces is proved: let \(0< q<\infty\) and let \(E\), \(F\) be quasi-Banach spaces. Let \((x_n)\) be a bounded sequence in the real interpolation space \(G:= (E,F)_{\theta,q}\) which tends to \(0\) in \(E+F\) but is bounded away from \(0\) in \(G\). Then there is a subsequence of \((x_n)\) whose closed linear span in \(G\) is isomorphic to \(\ell_q\). No motivation is provided. The proof is very technical.
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