Characterization of quasi-Banach spaces which coarsely embed into a Hilbert space
Abstract
A map f between two metric spaces (X,d1) and (Y,d2) is called a coarse embedding of X into Y if there exist two nondecreasing functions phi1, phi2:[0,∞) --> [0,∞) such that: phi1(d1(x,y)) ≤ d2(f(x),f(y)) ≤ phi2(d1(x,y)) for all x, y in X, and phi1(t) tends to ∞ as t tends to ∞. We characterize those quasi-Banach spaces that have a coarse embedding into a Hilbert space.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.