Some Parameterized Inequalities for g-Frames

The notion of g-frame is a generalization of that of frame. It has interested many mathematicians in recent years. In this paper, using the operator theory method, we obtained some parameterized inequalities for g-frames in Hilbert spaces. In the case of introducing parameters, we established an inequality for a g-frame and its canonical dual. And we obtained a converse inequality for a g-frame and its alternate duals. These obtained results generalize the existing ones.