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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.09638 |
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| _version_ | 1866917752033247232 |
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| author | Battseren, Bat-Od |
| author_facet | Battseren, Bat-Od |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09638 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $M_d$-multipliers of a locally compact group Battseren, Bat-Od Functional Analysis Group Theory 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. |
| title | $M_d$-multipliers of a locally compact group |
| topic | Functional Analysis Group Theory |
| url | https://arxiv.org/abs/2408.09638 |