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 orthogonal projection. At the end of paper, pre-frame operator of a dual frame is computed by pre-frame operator of a general ∗ -frame and an orthogonal projection.