The diameter of the isomorphism class of a Banach space

• Autores: William B. Johnson, Edward Odell
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 162, Nº 1, 2005, págs. 423-437
• Idioma: inglés
• DOI: 10.4007/annals.2005.162.423
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• Resumen

  • 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.