AN IMPRIMITIVITY TYPE THEOREM FOR INDUCED REPRESENTATIONS OF HILBERT MODULES

We reformulate the concepts of induced representations and Morita equivalence in the framework of Hilbert modules over pro-C*-algebras and give a module version of the imprimitivity theorem. Indeed, we show that for Morita equivalent Hilbert modules V and W over pro-C*-algebras A and B, respectively, there is a bijective correspondence between equivalence classes of non-degenerate representations of V and W.