On the isometrisability of group actions on p-spaces

2019/01/22 by Maria Gerasimova, Andreas Thom, Gerasimova, Maria +1
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1901.07496

openalex publication_date 2019/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we consider a p-isometrisability property of discrete groups. If p=2 this property is equivalent to unitarisability. We prove that any group containing a non-abelian free subgroup is not p-isometrisable for any p∈ (1, ∞). We also discuss some open questions and possible relations of p-isometrisability with the recently introduced Littlewood exponent \rm Lit(Γ).

Related

• Finitely approximable groups and actions Part I: The Ribes--Zalesski\uı property
• Locally compact groups with every isometric action bounded or proper
• Isometric actions on Lp-spaces: dependence on the value of p
• Isometrisable group actions
• Amenable groups and a geometric view on unitarisability