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Controlled frames which presented to improve the numerical output ofiterative algorithms for inverting the frame operator, have been introduced byBalazs and et al. Also, these frames are used by Bogdanova and et al. forspherical wavelets. In this note, we aim to study some new results aboutcontrolled fusion frames and behavior of them under erasures. Finally, we willintroduce the approximation operator for these frames and a result of thecomposition of the operators of two controlled fusion frames will be proved.

Robustness of controlled fusion frames under erasures of subspaces and the approximation operator