G-Frames for operators in Hilbert spaces

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.