TY - JOUR
ID - 34304
TI - Duals of Some Constructed $*$-Frames by Equivalent $*$-Frames
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Alijani, Azadeh
AD - Department of Mathematics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan, P.O. Box 7719758457, Rafsanjan, Iran.
Y1 - 2019
PY - 2019
VL - 13
IS - 1
SP - 165
EP - 177
KW - Dual frame
KW - Equivalent $*$-frame
KW - Frame operator
KW - $*$-frame
KW - Operator dual frame
DO - 10.22130/scma.2018.59232.206
N2 - 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.
UR - https://scma.maragheh.ac.ir/article_34304.html
L1 - https://scma.maragheh.ac.ir/article_34304_f1fa1d7d30cfa5a319737d9fba040b79.pdf
ER -