arXiv subjects

Aude Dalet

Publications and source records attributed to Aude Dalet.

4 recordsLinked to original sources

arXiv2018

Some properties of coarse Lipschitz maps between Banach spaces

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.

math.FA↗

arXiv2015

Characterization of metric spaces whose free space is isometric to $\ell_1$

We characterize metric spaces whose Lipschitz free space is isometric to $\ell_1$. In particular, the Lipschitz free space over an ultrametric space is not isometric to $\ell_1(Γ)$ for any set $Γ$. We give a lower bound for the Banach-Mazur distance in the finite case.

math.FA↗

arXiv2014

Free spaces over some proper metric spaces

We prove that the Lipschitz-free space over a countable proper metric space is isometric to a dual space and has the metric approximation property. We also show that the Lipschitz-free space over a proper ultrametric space is isometric to the dual of a space which is isomorphic to c_0.

math.FA↗

arXiv2014

Free Spaces over Countable Compact Metric Spaces

We prove that the Lipschitz-free space over a countable compact metric space is isometric to a dual space and has the metric approximation property.

math.FA↗