University of MaraghehSahand Communications in Mathematical Analysis2322-580708120171001$G$-Frames for operators in Hilbert spaces1212364610.22130/scma.2017.23646ENBahramDastourianDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, P.O. Box 1159-91775, Iran.MohammadJanfadaDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, P.O. Box 1159-91775, Iran.Journal Article20160625$K$-frames as a generalization of frames were introduced by L. Gu{a}vruc{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 ofÂ generalized $K$-frames, new results are investigatedÂ and some new perturbation results are established. Finally, we give several characterizations of $K$-duals.https://scma.maragheh.ac.ir/article_23646_5b6f187d7a7e622a7634cf56284bc2c6.pdf