Amenable unitary representations of locally compact groups

Summary A notion of amenability for an arbitrary unitary group representation is introduced. This unifies and generalizes the notions of amenable homogeneous spaces and of inner-amenable groups. Amenable locally compact groups are characterized by the amenability of all their unitary representations. Amenable representations are characterized by several properties which are operator theoretic analogues of properties characterizing amenable groups. We give a generalization to arbitrary representations of Hulanicki-Reiter theorem. This is used in order to describe the amenable representations of the groups with Kazhdan property (T).