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arXiv · 1705.00577

Asymptotic and coarse Lipschitz structures of quasi-reflexive Banach spaces

Gilles Lancien·Matias Raja
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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.

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Gilles Lancien, Matias Raja. 2017-05-01. Asymptotic and coarse Lipschitz structures of quasi-reflexive Banach spaces. https://arxiv.org/abs/1705.00577

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