The Diameter of the Isomorphism Class of a Banach Space

Details The Diameter of the Isomorphism Class of a Banach Space The Diameter of the Isomorphism Class of a Banach Space

2003-10-02

arxiv.org/abs/math/0310023v1

Mathematics

Functional Analysis

AMSLaTeX, 13 pages

Scientific paper

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 c_0. We call X elastic if for some K < infinity 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 < infinity every isomorph of X is K-elastic then X is finite dimensional.

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