Operator Characterizations and Some Properties of g-Frames on Hilbert Spaces

Given the g-orthonormal basis for Hilbert space H, we characterize the g-frames, normalized tight g-frames, and g-Riesz bases in terms of the g-preframe operators. Then we consider the transformations of g-frames, normalized tight g-frames, and g-Riesz bases, which are induced by operators and characterize them in terms of the operators. Finally, we discuss the sums and g-dual frames of g-frames by applying the results of characterizations.