A Morita type equivalence for dual operator algebras

We generalize the main theorem of Rieffel for Morita equivalence of W*-algebras to the case of unital dual operator algebras: two unital dual operator algebras image have completely isometric normal representations α,β such that image and image for a ternary ring of operators image (i.e. a linear space image such that image) if and only if there exists an equivalence functor imageF:AM→BM which “extends” to a *-functor implementing an equivalence between the categories image and image. By image we denote the category of normal representations of image and by image the category with the same objects as image and image-module maps as morphisms (image). We prove that this functor is equivalent to a functor “generated” by a image bimodule, and that it is normal and completely isometric.