On the uniform structure of separable \(\mathcal L_\infty\)-spaces (Q2444428)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the uniform structure of separable \(\mathcal L_\infty\)-spaces |
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On the uniform structure of separable \(\mathcal L_\infty\)-spaces (English)
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9 April 2014
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The first examples of separable uniformly homeomorphic \({\mathcal L}_\infty\)-spaces are found which are not isomorphic. Non-separable examples had been known for a long time. The proof is ingenious and quite flexible. Given any separable \({\mathcal L}_\infty\)-space \(X\), two uniformly homeomorphic separable \({\mathcal L}_\infty\)-spaces \(Y\) and \(Z\) are constructed so that \(Y\) has the Schur property and \(Z\) contains a complemented copy of \(X\). This opens the door to constructing large families of examples.
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uniform homeomorphism
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\(\mathcal L_\infty\)-space
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Banach space
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