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On the coarse geometry of James spaces

Authors
  • Lancien, Gilles
  • Petitjean, Colin
  • Procházka, Antonín
Type
Published Article
Publication Date
Nov 30, 2018
Submission Date
May 14, 2018
Identifiers
DOI: 10.4153/S0008439519000535
Source
arXiv
License
Yellow
External links

Abstract

In this note we prove that the Kalton interlaced graphs do not equi-coarsely embed into the James space $\mathcal J$ nor into its dual $\mathcal J^*$. It is a particular case of a more general result on the non equi-coarse embeddability of the Kalton graphs into quasi-reflexive spaces with a special asymptotic stucture. This allows us to exhibit a coarse invariant for Banach spaces, namely the non equi-coarse embeddability of this family of graphs, which is very close to but different from the celebrated property $\mathcal Q$ of Kalton. We conclude with a remark on the coarse geometry of the James tree space $\mathcal J \mathcal T$ and of its predual.

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