Some remarks on $M_d$-multipliers and approximation properties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915486976966656 |
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| author | Vergara, Ignacio |
| author_facet | Vergara, Ignacio |
| contents | We prove an extension property for $M_d$-multipliers from a subgroup to the ambient group, showing that $M_{d+1}(G)$ is strictly contained in $M_d(G)$ whenever $G$ contains a free subgroup. Another consequence of this result is the stability of the $M_d$-approximation property under group extensions. We also show that Baumslag-Solitar groups are $M_d$-weakly amenable with $\boldsymbolΛ(\operatorname{BS}(m,n),d)=1$ for all $d\geq 2$. Finally, we show that, for simple Lie groups with finite centre, $M_d$-weak amenability is equivalent to weak amenability, and we provide some estimates on the constants $\boldsymbolΛ(G,d)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07861 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some remarks on $M_d$-multipliers and approximation properties Vergara, Ignacio Group Theory Functional Analysis Operator Algebras We prove an extension property for $M_d$-multipliers from a subgroup to the ambient group, showing that $M_{d+1}(G)$ is strictly contained in $M_d(G)$ whenever $G$ contains a free subgroup. Another consequence of this result is the stability of the $M_d$-approximation property under group extensions. We also show that Baumslag-Solitar groups are $M_d$-weakly amenable with $\boldsymbolΛ(\operatorname{BS}(m,n),d)=1$ for all $d\geq 2$. Finally, we show that, for simple Lie groups with finite centre, $M_d$-weak amenability is equivalent to weak amenability, and we provide some estimates on the constants $\boldsymbolΛ(G,d)$. |
| title | Some remarks on $M_d$-multipliers and approximation properties |
| topic | Group Theory Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2509.07861 |