@article { author = {Mirzaee Azandaryani, Morteza}, title = {Approximate Duals of $g$-frames and Fusion Frames in Hilbert $C^\ast-$modules}, journal = {Sahand Communications in Mathematical Analysis}, volume = {15}, number = {1}, pages = {135-146}, year = {2019}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {10.22130/scma.2018.81624.396}, abstract = {In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^\ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and fusion frames to Hilbert $C^\ast-$modules, where $Q$ is an adjointable operator, and obtain some properties of this kind of approximate duals.}, keywords = {Frame,G-Frame,Fusion frame,Biorthogonal sequence,Approximate duality}, url = {https://scma.maragheh.ac.ir/article_35726.html}, eprint = {https://scma.maragheh.ac.ir/article_35726_cc21d1f5aa898076fe219206175ae0ca.pdf} }