The Rao–Reiter Criterion for the Amenability of Homogeneous Spaces

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Abstract

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).

Original languageEnglish
Pages (from-to)1094-1099
Number of pages6
JournalSiberian Mathematical Journal
Volume59
Issue number6
DOIs
Publication statusPublished - 1 Nov 2018

Keywords

  • amenability
  • homogeneous space
  • locally compact group
  • N-function
  • Orlicz space
  • Δ-condition
  • Delta(2)-condition

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