$M_d$-multipliers of a locally compact group

Bat-Od Battseren

$M_d$-multipliers of a locally compact group

Functional Analysis 2024-08-20 v1 Group Theory

Authors: Bat-Od Battseren

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.

Keywords

M_d-multipliers Locally Compact Group Haagerup Tensor Product Banach Space Isometric Isomorphism Approximation Properties Convolution Map Dual Space

Cite

@article{arxiv.2408.09638,
  title  = {$M_d$-multipliers of a locally compact group},
  author = {Bat-Od Battseren},
  journal= {arXiv preprint arXiv:2408.09638},
  year   = {2024}
}

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13 pages

$M_d$-multipliers of a locally compact group

Abstract

Keywords

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