C*-convex sets and completely hounded bimodule homomorphisms

If A and B are C*-algebras and X is an operator A, B-bimodule, then points of X can be separated from closed A, B-absolutely convex subsets of X by co mpletely bounded A, B-bimodule homomorphisms from X into B(K), where K is a Hilbert space and the A, B-bimodule structure on B(IC) is induced by a pai r of representations pi : A --> B(K) and sigma : B --> B(K). If A and B are von Neumann algebras and X is a normal (not necessarily dual) operator A, B-bimodule, those A, B-absolutely convex subsets of X are characterized whi ch can be separated from points of X as above, but with the additional requ irement that the two representations pi and sigma are normal. This requires a new topology on X, which has appeared also in connection with some other questions concerning operator modules.