  In this paper we introduce the concept of von Neumann-Schatten Bessel
multipliers and obtain some of their characterizations. Finally, special
attention is devoted to the study of invertible Hilbert--Schmidt frame
multipliers. These results are not only of interest in their own right, but
also they pave the way for obtaining some new results for diagonalization of
matrices in finite dimensional setting as well as for dual $g$-frames. In
particular, we show that a $g$-frame is uniquely determined by the set of its
$g$-frames.
