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Let $\Phi$ and $\Psi$ be frames for $\cal H$ and let $M_{m,\Phi,\Psi}$ be aframe multiplier with the symbol $m$. In this paper, we restrict ourinvestigation to show that the operator properties of $M_{m,\Phi,\Psi}$ arestable under the perturbations of $\Phi$, $\Psi$ and $m$. Also, specialattention is devoted to the study of invertible frame multipliers. Theseresults are not only of interest in their own right, but also they pave the wayfor obtaining some new results for Gabor multipliers which have been studiedmostly by Hans Georg Feichtinger and his coauthors in recent years.

Invariances of the operator properties of frame multipliers under perturbations of frames and symbol