Alijani, A. (2019). Duals of Some Constructed $*$-Frames by Equivalent $*$-Frames. Sahand Communications in Mathematical Analysis, 13(1), 165-177. doi: 10.22130/scma.2018.59232.206

Azadeh Alijani. "Duals of Some Constructed $*$-Frames by Equivalent $*$-Frames". Sahand Communications in Mathematical Analysis, 13, 1, 2019, 165-177. doi: 10.22130/scma.2018.59232.206

Alijani, A. (2019). 'Duals of Some Constructed $*$-Frames by Equivalent $*$-Frames', Sahand Communications in Mathematical Analysis, 13(1), pp. 165-177. doi: 10.22130/scma.2018.59232.206

Alijani, A. Duals of Some Constructed $*$-Frames by Equivalent $*$-Frames. Sahand Communications in Mathematical Analysis, 2019; 13(1): 165-177. doi: 10.22130/scma.2018.59232.206

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

^{}Department of Mathematics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan, P.O. Box 7719758457, Rafsanjan, Iran.

Abstract

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.