On some questions of Eymard and Bekka concerning amenability of homogeneous spaces and induced representations

Abstract

Let $F\subseteq H\subseteq G$ be closed subgroups of a locally compact group. In response to a 1972 question by Eymard, we construct an example where the homogeneous factor-space $G/F$ is amenable in the sense of Eymard-Greenleaf, while $H/F$ is not. (In our example, $G$ is discrete.) As a corollary which answers a 1990 question by Bekka, the induced representation $\ind_H^G(ρ)$ can be amenable in the sense of Bekka even if $\rho$ is not amenable. The second example, answering another question by Bekka, shows that $\ind_H^G(ρ)$ need not be amenable even if both the representation $\rho$ and the coset space $G/H$ are amenable.

6 pages, LaTeX 2e, to appear in: C.R.Math.Rep.Acad.Sci.Canada

References in corpus (1)

• On co-amenability for groups and von Neumann algebras

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