Non-trivial lamplighters over non-amenable groups are non-unitarizable

It was proved by Ozawa and Monod that a wreath products of a group containing an infinite abelian subroup and a non-amenable group is non-unitarizable. We show that a wreath product of a non-trivial group and a non-amenable group is non-unitarizable.Comment: 9 page

The invariant random order extension property is equivalent to amenability

Recently, Glasner, Lin and Meyerovitch gave a first example of a partial invariant order on a certain group that cannot be invariantly extended to an invariant random total order. Using their result as a starting point we prove that any invariant random partial order on a countable group could be invariantly extended to an invariant random total order iff the group is amenable.Comment: 16 pages, added references, fixed typo