We give a contractive Schur multiplier characterization of locally compact groups coarsely embeddable into Hilbert spaces. Consequently, all locally compact groups whose weak Haagerup constant is 1 embed coarsely into Hilbert spaces, and hence the Baum-Connes assembly map with coefficients is split-injective for such groups.
"A Schur multiplier characterization of coarse embeddability." Bull. Belg. Math. Soc. Simon Stevin 22 (3) 403 - 409, august 2015. https://doi.org/10.36045/bbms/1442364587