  G-frames are generalized frames which include ordinary frames, bounded
invertible linear operators, as well as many recent generalizations of frames,
e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural
generalizations of frames and provide more choices on analyzing functions from
frame expansion coefficients. We give characterizations of g-frames and prove
that g-frames share many useful properties with frames. We also give
generalized version of Riesz bases and orthonormal bases. As an application, we
get atomic resolutions for bounded linear operators.
