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The Diameter of the Isomorphism Class of a Banach Space

W. B. Johnson and E. Odell
Annals of Mathematics
Second Series, Vol. 162, No. 1 (Jul., 2005), pp. 423-437
Published by: Annals of Mathematics
Stable URL: http://www.jstor.org/stable/3597376
Page Count: 15
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The Diameter of the Isomorphism Class of a Banach Space
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Abstract

We prove that if X is a separable infinite dimensional Banach space then its isomorphism class has infinite diameter with respect to the Banach-Mazur distance. One step in the proof is to show that if X is elastic then X contains an isomorph of c0. 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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