Dixmier traces on noncompact isospectral deformations

We extend the isospectral deformations of Connes, Landi and Dubois-Violette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group Rl. Under deformation by a torus action, a standard formula relates Dixmier traces of measurable operators to integrals of functions on the manifold. We show that this relation persists for actions of Rl, under mild restrictions on the geometry of the manifold which guarantee the Dixmier traceability of those operators.