  We investiguate a property of affine isometric actions on Hilbert spaces
called evanescence. Evanescent actions are the extreme opposite of irreducible
actions. Every affine isometric action decomposes naturally into an evanescent
part and an irreducible part. We study when this decomposition is unique. We
also study when an action that has almost fixed points is automatically
evanescent. We relate these questions to the identity excluding property for
groups. We also relate them to the finiteness of the von Neumann algebras
generated by the linear part of the action.
