Takesaki-Takai Duality Theorem in Hilbert C*-Modules

In this paper, we generalize the Takesaki-Takai duality theorem in Hilbert C*-modules; that is to say, if (H, V, U) is a Kac-system, where H is a Hilbert space, V is a multiplicative unitary operator on H circle times H and U is a unitary operator on H, and if E is an L-compatible Hilbert A-module, then E x L x L similar or equal to E circle times K (H), where K (H) is the set of all compact operators on H, and L and L are Hopf C*-algebras corresponding to the Kac-system (H, V, U).