On some questions of Eymard and Bekka concerning amenability of homogeneous spaces and induced representations
Abstract
Description
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 $ρ$ 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 $ρ$ and the coset space $G/H$ are amenable.
6 pages, LaTeX 2e, to appear in: C.R.Math.Rep.Acad.Sci.Canada
6 pages, LaTeX 2e, to appear in: C.R.Math.Rep.Acad.Sci.Canada