Bulletin of the Belgian Mathematical Society - Simon Stevin

A Schur multiplier characterization of coarse embeddability

Søren Knudby and Kang Li

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Abstract

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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 3 (2015), 403-409.

Dates
First available in Project Euclid: 16 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1442364587

Digital Object Identifier
doi:10.36045/bbms/1442364587

Mathematical Reviews number (MathSciNet)
MR3396991

Zentralblatt MATH identifier
1334.43004

Subjects
Primary: 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 43A35: Positive definite functions on groups, semigroups, etc. 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]

Keywords
Coarse embedding Schur multipliers Baum-Connes conjecture

Citation

Knudby, Søren; Li, Kang. A Schur multiplier characterization of coarse embeddability. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 3, 403--409. doi:10.36045/bbms/1442364587. https://projecteuclid.org/euclid.bbms/1442364587


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