Some remarks on $M_d$-multipliers and approximation properties

Fuente: arXiv
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Main Author: Vergara, Ignacio
Format: Preprint
Published: 2025
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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