The diameter of the isomorphism class of a Banach space
成果类型：
Article
署名作者：
Johnson, WB; Odell, E
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2005.162.423
发表日期：
2005
页码：
423-437
关键词：
摘要：
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.