Characterization of quasi-Banach spaces which coarsely embed into a Hilbert space

2004/11/11 by N. L. Randrianarivony, Randrianarivony, N. L.
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #math.FA #math.MG

paper · pdf · doi:10.48550/arxiv.math/0411269

3 pages

arxiv created 2004/11/11 · arxiv updated 2009/12/01

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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