University of MaraghehSahand Communications in Mathematical Analysis2322-580710120180401Similar generalized frames17282462810.22130/scma.2017.24628ENAzadeh AlijaniDepartment of Mathematics, Faculty of Science,
Vali-e-Asr University of Rafsanjan, P.O. Box 7719758457, Rafsanjan, Iran.Journal Article20160915Generalized frames are an extension of frames in HilbertĀ spaces andĀ Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an orthogonal projection. Moreover, a $g$-frame is obtained by two the $g$-frames and its operator duals are investigated. Finally, the dilation of $g$-frames is studied.http://scma.maragheh.ac.ir/article_24628_6e243f25a60fbae52edb2214bfc74bcd.pdf