Abstract
We introduce here the notion of superstable Banach space, as the superproperty associated with the stability property of J. L. Krivine and B. Maurey. IfE is superstable, so are theL p (E) for eachp∈[1, +∞[. If the Banach spaceX uniformly imbeds into a superstable Banach space, then there exists an equivalent invariant superstable distance onX; as a consequenceX contains subspaces isomorphic tol p spaces (for somep∈[1, ∞[). We give also a generalization of a result of P. Enflo: the unit ball ofc 0 does not uniformly imbed into any stable Banach space.
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