Coarse embeddability into Banach spaces

Abstract

The main purposes of this paper are (1) To survey the area of coarse embeddability of metric spaces into Banach spaces, and, in particular, coarse embeddability of different Banach spaces into each other; (2) To present new results on the problems: (a) Whether coarse non-embeddability into ${\ell }_2$ implies presence of expander-like structures? (b) To what extent ${\ell }_2$ is the most difficult space to embed into?

23 pages

References in corpus (1)

• Euclidean quotients of finite metric spaces

Cited by in corpus (1)

• Expansion properties of metric spaces not admitting a coarse embedding into a Hilbert space