G-Riesz frames in Hilbert spaces

G-frames,which were proposed recently as generalized frames in Hilbert spaces,share many similar properties with frames,but not all the properties of them are similar.Christensen presented that every Riesz frame contains a Riesz basis.In this paper,the authors showed that not all g-Riesz frames contain a g-Riesz basis,but they obtained that every g-Riesz frame contains an exact g-frame.They also gave a necessary and sufficient condition for a g-Riesz frame in a Hilbert space.From this,they might get the characterization of Riesz frames.Lastly the authors considered the stability of a g-Riesz frame for a Hilbert space under perturbations.These properties of g-Riesz frames in Hilbert spaces are not similar to those of Riesz frames.