Hilbert C*-modules with a predual

We extend Sakai's characterization of von Neumann algebras to the context of Hilbert C*-modules. If A, B are C*-algebras and X is a full Hilbert A-B-bimodule possessing a predual such that left, respectively right, multiplications are weak*-continuous, then M(A) and M(B) are W*-algebras, the predual is unique, and X is selfdual in the sense of Paschke. For unital A, B the above continuity requirement is automatic. We determine the dual Banach space X* of a Hilbert A-B-bimodule X and show that Paschke's selfdual completion of X is isomorphic to the bidual X**, which is a Hilbert C*-module in a natural way. We conclude with a new approach to multipliers of Hilbert C*-bimodules.