%0 Journal Article
%T Duals of Some Constructed $*$-Frames by Equivalent $*$-Frames
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Alijani, Azadeh
%D 2019
%\ 02/01/2019
%V 13
%N 1
%P 165-177
%! Duals of Some Constructed $*$-Frames by Equivalent $*$-Frames
%K Dual frame
%K Equivalent $*$-frame
%K Frame operator
%K $*$-frame
%K Operator dual frame
%R 10.22130/scma.2018.59232.206
%X 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.
%U https://scma.maragheh.ac.ir/article_34304_f1fa1d7d30cfa5a319737d9fba040b79.pdf