  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 .
