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 (2)

• Metric Cotype
• Euclidean quotients of finite metric spaces

Cited by in corpus (7)

• Relative expanders
• Coarse and uniform embeddings
• On embeddings of locally finite metric spaces into ${\ell }_p$
• Expansion properties of metric spaces not admitting a coarse embedding into a Hilbert space
• Embeddings of proper metric spaces into Banach spaces
• A duality operators/Banach spaces
• Embeddability of locally finite metric spaces into Banach spaces is finitely determined