This is an announcement for the paper "$\ell_p$ (p>2) does not coarsely embed into a Hilbert space" by W. B. Johnson and N. L. Randrianarivony.

Abstract: 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<p<\infty.

Archive classification: Functional Analysis

Remarks: 10 pages

The source file(s), coarselpl2.9.tex: 14916 bytes, is(are) stored in gzipped form as 0410427.gz with size 5kb. The corresponding postcript file has gzipped size 36kb.

Submitted from: nirina@math.tamu.edu

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