Some results about operator perturbation of fusion frames in Hilbert spaces

The stabilities of fusion frames under operator perturbation (simple named operator perturbation of the fusion frames), is the study object of this paper. We provide a way as follows for studying the operator perturbation of fusion frames. Firstly, we consider the operator perturbation of fusion frame sequences by the gap between two closed subspaces and discuss the relationships between the operator perturbation of fusion frames and the operator perturbation of fusion frame sequences. Lastly, we transform the operator perturbation of fusion frames into the operator perturbation of fusion frame sequences based on these relationships. Our results obtained this way generalize the remarkable results which have been obtained by Casazza, Kutyniok, Asgari, Gavruta and Zhu.