A note on perturbations of fusion frames

Abstract In this work, we consider some relationships between a closed range operator T and a fusion frame W = ( W i , w i ) i ∈ I for a Hilbert space H that provides that the sequence ( T ( W i ) ‾ , v i ) i ∈ I is a fusion frame sequence for H , if we consider a suitable family of weights { v i } i ∈ I . This (sufficient) condition generalizes some previous work in the subject.