@article { author = {Dastourian, Bahram and Janfada, Mohammad}, title = {$G$-Frames for operators in Hilbert spaces}, journal = {Sahand Communications in Mathematical Analysis}, volume = {08}, number = {1}, pages = {1-21}, year = {2017}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {10.22130/scma.2017.23646}, abstract = {$K$-frames as a generalization of frames were introduced by L. G\u{a}vru\c{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new generalization of $K$-frames. After proving some characterizations of  generalized $K$-frames, new results are investigated  and some new perturbation results are established. Finally, we give several characterizations of $K$-duals.}, keywords = {$g$-atomic system,$g$-$K$-frame,$g$-$K$-dual,Perturbation}, url = {https://scma.maragheh.ac.ir/article_23646.html}, eprint = {https://scma.maragheh.ac.ir/article_23646_5b6f187d7a7e622a7634cf56284bc2c6.pdf} }