This is an announcement for the paper “Some properties of coarse Lipschitz maps between Banach spaces” by Aude Dalethttps://arxiv.org/find/math/1/au:+Dalet_A/0/1/0/all/0/1, Gilles Lancienhttps://arxiv.org/find/math/1/au:+Lancien_G/0/1/0/all/0/1.
Abstract: We study the structure of the space of coarse Lipschitz maps between Banach spaces. In particular we introduce the notion of norm attaining coarse Lipschitz maps. We extend to the case of norm attaining coarse Lipschitz equivalences, a result of G. Godefroy on Lipschitz equivalences. This leads us to include the non separable versions of classical results on the stability of the existence of asymptotically uniformly smooth norms under Lipschitz or coarse Lipschitz equivalences.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1612.01364