In this paper we consider the following problem: When are the preduals of two hyperfinite (=injective) factors M and N (on separable Hilbert spaces) cb-isomorphic (i.e., isomorphic as operator spaces)? We show that if M is semifinite and N is type III, then their preduals are not cb-isomorphic. Moreover, we construct a one-parameter family of hyperfinite… (More)