Espaces de Banach superstables, distances stables et homeomorphismes uniformes. (French) Zbl 0537.46023
The superproperty associated with the notion of stable Banach spaces is investigated.
The author proves \(L_ p(E)\) is superstable if and only if E is superstable. Moreover properties of Banach spaces that uniformly imbed in a superstable Banach space are studied; in particular, it is proved that such a space contains, for some real p an isomorphic copy of \(\ell_ p\).
The author proves \(L_ p(E)\) is superstable if and only if E is superstable. Moreover properties of Banach spaces that uniformly imbed in a superstable Banach space are studied; in particular, it is proved that such a space contains, for some real p an isomorphic copy of \(\ell_ p\).
Reviewer: J.-Th.Lapreste
MSC:
| 46B20 | Geometry and structure of normed linear spaces |
| 46B25 | Classical Banach spaces in the general theory |
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