Embeddings of proper metric spaces into Banach spaces

Abstract

We show that there exists a strong uniform embedding from any proper metric space into any Banach space without cotype. Then we prove a result concerning the Lipschitz embedding of locally finite subsets of ${\mathcal{L}}_p$-spaces. We use this locally finite result to construct a coarse bi-Lipschitz embedding for proper subsets of any ${\mathcal{L}}_p$-space into any Banach space $X$ containing the ${\ell }_p^n$'s. Finally using an argument of G. Schechtman we prove that for general proper metric spaces and for Banach spaces without cotype a converse statement holds.

16 pages

References in corpus (3)

• Metric Cotype
• Coarse embeddability into Banach spaces
• Remarks on quasi-isometric non-embeddability into uniformly convex Banach spaces

Cited by in corpus (1)

• Tight embeddability of proper and stable metric spaces