  K-frame theory was recently introduced to reconstruct elements from the range
of a bounded linear operator K in a separable Hilbert space. This significant
property is worthwhile especially in some problems arising in sampling theory.
Some equalities and inequalities have been established for ordinary frames and
their duals. In this paper, we continue and extend these results to obtain
several important equalities and inequalities for K-frames. Moreover, by
applying Jensen's operator inequality we obtain some new inequalities for
$K$-frames.
