Characterization of quasi-Banach spaces which coarsely embed into a Hilbert space
N. L. Randrianarivony
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.
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