Duals of Some Constructed *-Frames by Equivalent *-Frames

Hilbert frames theory have been extended to frames in Hilbert C * -modules. The paper introduces equivalent *-frames and presents ordinary duals of a constructed *-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that *-frames and ordinary duals or operator duals of another *-frames are equivalent under these conditions. We obtain a *-frame by an orthogonal projection and a given *-frame, characterize its duals, and give a bilateral condition for commutating frame operator of a primary *-frame and an or- thogonal projection. At the end of paper, preframe operator of a dual frame is computed by preframe operator of a general *-frame and an orthogonal projection.