University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201Duals of Some Constructed $*$-Frames by Equivalent $*$-Frames1651773430410.22130/scma.2018.59232.206ENAzadehAlijaniDepartment of Mathematics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan, P.O. Box 7719758457, Rafsanjan, Iran.Journal Article20170215Hilbert 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.https://scma.maragheh.ac.ir/article_34304_f1fa1d7d30cfa5a319737d9fba040b79.pdf