Splitting of operator for frame inequalities in Hilbert spaces

In this paper, we obtain a new type of inequalities for frames, which are parametrized by a parameter \lambda\in R . By suitable choices of {\lambda}, one obtains the previous results as special cases. Our new proof also makes the underlying mathematical structure that gives rise to these inequalities more transparent than previous approaches: Our proof shows that the main point is the splitting S = S1 + S2 of the positive denite frame operator S into the two positive semidenite operators S1 and S2 .