On Co-amenability for Groups and Von Neumann Algebras
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چکیده
We first show that co-amenability does not pass to subgroups, answering a question asked by Eymard in 1972. We then address address coamenability for von Neumann algebras, describing notably how it relates to the former. Co-amenable subgroups A subgroup H of a group G is called co-amenable in G if it has the following relative fixed point property: Every continuous affine G-action on a convex compact subset of a locally convex space with an H-fixed point has a G-fixed point. This is equivalent to the existence a G-invariant mean on the space l(G/H) or to the weak containment of the trivial representation in l(G/H), see [4] (compare also Proposition 5 below). Alternative terminology is amenable pair or coFølner, and more generally Greenleaf [5] introduced the notion of an amenable action (conflicting with more recent terminology) further generalized by Zimmer [10] to amenable pairs of actions. In the particular case of a normal subgroup H ⊳G, co-amenability is equivalent to amenability of the quotient G/H . One checks that for a triple
منابع مشابه
Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras
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