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Let $\mathcal{X}$ be a finite-dimensional complex vector space and let k be apositive integer. An explicit formula for the k-reflexivity defect of the imageof a generalized derivation on $L(\mathcal{X})$, the space of all lineartransformations on $\mathcal{X}$, is given. Using latter, we also study thek-reflexivity defect of the image of an elementary operator of the form$\Delta(T)=ATB-T$ $(T \in L(\mathcal{X}))$.

$k$-reflexivity defect of the image of a generalized derivation