Geodesic
On the Coarse Geometry of James Spaces
Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 77-93

Voir la notice de l'article provenant de la source Cambridge University Press

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 ${\mathcal{J}}^{\ast }$. 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 structure. 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.
DOI : 10.4153/S0008439519000535
Mots-clés : non linear geometry of Banach space, coarse embedding, James space 
Lancien, Gilles; Petitjean, Colin; Procházka, Antonin. On the Coarse Geometry of James Spaces. Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 77-93. doi: 10.4153/S0008439519000535
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