Yet another short proof of Bourgain’s distortion estimate for embedding of trees into uniformly convex Banach spaces

Benoît Kloeckner (1)

1 IF - Institut Fourier

We use a self-improvement argument to give a very short and elementary proof of the result of Bourgain saying that regular trees do not admit bi-Lipschitz embeddings into uniformly convex Banach spaces.

Mots clés: uniformly convex spaces; Banach spaces; trees; Hilbert space; bi-Lipschitz embeddings; distorsion

Domaines: Analyse fonctionnelle [math.FA]; Géométrie métrique [math.MG]

Benoît Kloeckner. Yet another short proof of Bourgain’s distortion estimate for embedding of trees into uniformly convex Banach spaces. Israel Journal of Mathematics, 2014, 200 (1), pp.419-422. ⟨10.1007/s11856-014-0024-4⟩. ⟨hal-00785961⟩