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

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

2002-12-30

arxiv.org/abs/math/0212380v6

C.R. Math. Rep. Acad. Sci. Canada 25 (2003), 76-81.

Mathematics

Operator Algebras

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

Scientific paper

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 $\ind_H^G(\rho)$ can be amenable in the sense of Bekka even if $\rho$ is not amenable. The second example, answering another question by Bekka, shows that $\ind_H^G(\rho)$ need not be amenable even if both the representation $\rho$ and the coset space $G/H$ are amenable.

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