The Rao–Reiter Criterion for the Amenability of Homogeneous Spaces

Сибирский математический журнал

Ya. A. Kopylov¹ 

[1] Novosibirsk State University

关键词: locally compact group;    homogeneous space;    amenability;    N-function;    Orlicz space;    Δ2-condition;   

DOI  :  10.1134/S0037446618060125

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

We prove that a homogeneous space G/H, with G a locally compact group and H a closed subgroup of G, is amenable in the sense of Eymard–Greenleaf if and only if the quasiregular action πΦ of G on the unit sphere of the Orlicz space LΦ(G/H) for some N-function Φ ∈ Δ2 satisfies the Rao–Reiter condition (PΦ).

【 授权许可】

CC BY