This is an announcement for the paper “Asymptotic and coarse Lipschitz structures of quasi-reflexive Banach spaces” by Gilles Lancienhttps://arxiv.org/find/math/1/au:+Lancien_G/0/1/0/all/0/1, Matias Rajahttps://arxiv.org/find/math/1/au:+Raja_M/0/1/0/all/0/1.

Abstract: In this note, we extend to the setting of quasi-reflexive spaces a classical result of N. Kalton and L. Randrianarivony on the coarse Lipschitz structure of reflexive and asymptotically uniformly smooth Banach spaces. As an application, we show for instance, that for $1\leq q<p$, 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.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1705.00577