  In a recent paper of the first author and Kashyap, a new class of modules
over dual operator algebras is introduced. These generalize the W*-modules
(that is, Hilbert C*-modules over a von Neumann algebra which satisfy an
analogue of the Riesz representation theorem for Hilbert spaces), which in turn
generalize the theory of Hilbert spaces. In the present paper we give several
new results about these modules.
