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arXiv · 2408.09638

$M_d$-multipliers of a locally compact group

Bat-Od Battseren
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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 to lattices.

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Bat-Od Battseren. 2024-08-19. $M_d$-multipliers of a locally compact group. https://arxiv.org/abs/2408.09638

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