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Article Dans Une Revue Canadian Mathematical Bulletin Année : 2020

On the Coarse Geometry of James Spaces

Résumé

In this note we prove that the Kalton interlaced graphs do not equi-coarsely embed into the James space J nor into its dual 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 Q of Kalton. We conclude with a remark on the coarse geometry of the James tree space J T and of its predual.
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Dates et versions

hal-02373870 , version 1 (21-11-2019)

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G. Lancien, Colin Petitjean, Antonin Prochazka. On the Coarse Geometry of James Spaces. Canadian Mathematical Bulletin, 2020, 63 (1), pp.77-93. ⟨10.4153/S0008439519000535⟩. ⟨hal-02373870⟩
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