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arXiv · 1805.05171

On the coarse geometry of James spaces

Gilles Lancien·Colin Petitjean·Antonín Procházka
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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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Gilles Lancien, Colin Petitjean, Antonín Procházka. 2018-05-14. On the coarse geometry of James spaces. https://doi.org/10.4153/s0008439519000535

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