$M_{d}$-multipliers of a locally compact group

Bat-Od Battseren

doi:10.4171/ggd/957

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$M_{d}$ -multipliers of a locally compact group

Bat-Od Battseren
Vanderbilt University, Nashville, USA

$$M_{d}$-multipliers of a locally compact group cover$

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Abstract

We show that the space $M_{d} (G)$ of $M_{d}$ -multipliers of a locally compact group $G$ is isometrically isomorphic to the Banach space of bounded functionals on the $d$ -fold Haagerup tensor product of $L^{1} (G)$ vanishing on the kernel of the convolution map. Consequently, we see that $M_{d} (G)$ is isometrically isomorphic to the dual space of $X_{d} (G)$ , the completion of $L^{1} (G)$ in the dual of $M_{d} (G)$ . We also show that $M_{d}$ -type approximation properties are inherited by lattices.

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Bat-Od Battseren, $M_{d}$ -multipliers of a locally compact group. Groups Geom. Dyn. (2026), published online first

DOI 10.4171/GGD/957