Asymptotic and coarse Lipschitz structures of quasi-reflexive Banach spaces
Résumé
In this note, we extend to the setting of quasi-reflexive spaces a classical result of N. Kalton and L. Randrianarivony on the coarse Lip-schitz structure of reflexive and asymptotically uniformly smooth Banach spaces. As an application, we show for instance, that for 1 ≤ q < p, a q-asymptotically uniformly convex Banach space does not coarse Lipschitz embed into a p-asymptotically uniformly smooth quasi-reflexive Banach space. This extends a recent result of B.M. Braga.
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