Amenability of Hecke pairs and a question of Eymard

Abstract

In this short paper we show that if $(G,H)$ is an amenable Hecke pair and $\Gamma$ is a subgroup of $G$ containing $H$, then the Hecke pair $(\Gamma ,H)$ is amenable too. This answers positively a question of Pierre Eymard, asked in 1972, when it is restricted to Hecke pairs

I modified the proof of Theorem 7, added some explanations, and updated the references. (6 pages)

References in corpus (4)

• On co-amenability for groups and von Neumann algebras
• On some questions of Eymard and Bekka concerning amenability of homogeneous spaces and induced representations
• Commensurated subgroups of arithmetic groups, totally disconnected groups and adelic rigidity
• Locally compact Hecke pairs

Cited by in corpus (2)

• Locally compact Hecke pairs
• Length functions and property (RD) for locally compact Hecke pairs