Tree metrics and their Lipschitz-free spaces

By Alexandre Godard. 2009

94 citations recorded by the source corpus.

We compute the Lipschitz-free spaces of subsets of the real line and characterize subsets of metric trees by the fact that their Lipschitz-free space is isometric to a subspace of $L_1$.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/341771ffa3cf8f29bb971d0f4aeb4abde9b107cb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The non-linear geometry of Banach spaces after Nigel Kalton (2012, unknown): “metric spaces M whose free space is isometric to a subspace of L1 are characterized in [31] as subsets of metric trees equipped with the least path metric.”
Approximation properties and Schauder decompositions in Lipschitz-free spaces (2012, unknown): “15 83 v1 [ m at h. FA ] 6 J ul”
On the structure of Lipschitz-free spaces (2015, background): “For example, if M ⊂ R is a set of measure zero or if M is a separable ultrametric space, then F(M) is isomorphic to 1; see [13] and [7].”
On strongly norm attaining Lipschitz maps (2018, methodology): “F(M) is isometric to `1 by [20], so it clearly has property α.”
Free Spaces Over Some Proper Metric Spaces (2014, background): “[4] A. Godard, Tree metrics and their Lipschitz-free spaces, Proc.”