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

Multipliers for von Neumann-Schatten Bessel sequences in separable Banach spaces