$\ell_p$ (p>2) does not coarsely embed into a Hilbert space

Details $\ell_p$ (p>2) does not coarsely embed into a Hilbert space $\ell_p$ (p>2) does not coarsely embed into a Hilbert space

2004-10-19

arxiv.org/abs/math/0410427v1

Mathematics

Functional Analysis

10 pages

Scientific paper

A coarse embedding of a metric space X into a metric space Y is a map f: X-->Y satisfying for every x, y in X: \phi_1(d(x,y)) \leq d(f(x),f(y)) \leq \phi_2(d(x,y)) where \phi_1 and \phi_2 are nondecreasing functions on [0,\infty) with values in [0,\infty), with the condition that \phi_1(t) tends to \infty as t tends to \infty. We show that \ell_p does not coarsely embed in a Hilbert space for 2

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