Some remarks on M_d-multipliers and approximation properties

2025/09/09 by Vergara, Ignacio
#FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2509.07861

Abstract

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(BS(m,n),d)=1 for all d≥ 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).

Citations

• Property (T) for uniformly bounded representations and weak*-continuity of invariant means
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Related

• The Strong Approximation Conjecture holds for amenable groups
• On arithmetic properties of solvable Baumslag-Solitar groups
• (Non-)amenability of the Fourier algebra in the cb-multiplier norm
• A Survey of Amenability Theory for Direct-Limit Groups
• Approximate subgroups and super-strong approximation