Geodesic
The diameter of the isomorphism class of a Banach space
William B. Johnson1 ; Edward Odell2
1 Department of Mathematics, Texas A & M University, College Station, TX 77843, United States
2 Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, United States
Annals of mathematics, Tome 162 (2005) no. 1, pp. 423-437.

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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 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 $K <\infty$ 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 $K\lt \infty$ every isomorph of $X$ is $K$-elastic then $X$ is finite dimensional.
DOI : 10.4007/annals.2005.162.423

William B. Johnson 1 ; Edward Odell 2

1 Department of Mathematics, Texas A & M University, College Station, TX 77843, United States
2 Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, United States 
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William B. Johnson; Edward Odell. The diameter of the isomorphism class of a Banach space. Annals of mathematics, Tome 162 (2005) no. 1, pp. 423-437. doi : 10.4007/annals.2005.162.423. http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.162.423/

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