G-frames for operators in Hilbert spaces

K-frames as a generalization of frames were introduced by L. G avrut a to study atomic systems on Hilbert spaces which al- lows, 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 di er- ence 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 char- acterizations of K-duals.

Keywords:

g-atomic system , g-K-frame , g-K-dual , Perturbation