Asymptotic and coarse Lipschitz structures of quasi-reflexive Banach spaces

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 $1\le q<p$, 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.

12 pages

References in corpus (1)

• Asymptotic structure and coarse Lipschitz geometry of Banach spaces

Cited by in corpus (2)

• On the coarse geometry of James spaces
• Banach spaces with the Blum-Hanson Property