English

Some properties of coarse Lipschitz maps between Banach spaces

Functional Analysis 2018-12-12 v3

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.

Keywords

Cite

@article{arxiv.1612.01364,
  title  = {Some properties of coarse Lipschitz maps between Banach spaces},
  author = {Aude Dalet and Gilles Lancien},
  journal= {arXiv preprint arXiv:1612.01364},
  year   = {2018}
}

Comments

The proof of Prposition 4.6 has been corrected, as well as the statement of Prposition 2.2