Author:
Lancien Gilles,Petitjean Colin,Procházka Antonin
Abstract
AbstractIn 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.
Publisher
Canadian Mathematical Society
Cited by
2 articles.
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