The diameter of the isomorphism class of a Banach space
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We prove that if X is a, separable infinite dimensional Banach space then its isomorphism class has infinite diameter with respect to the Banaeh-Mazur distance. One step in the proof is to show that if X is elastic then X contains an isomorph of C 0 . We call X elastic if for some K < ∞ for every Banach space Y which embeds into X, the space Y is K-isomorphic to a subspace of X. We also prove that if X is a separable Banach space such that for some K < ∞ every isomorph of X is K-elastic then X is finite dimensional.
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