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 $\mathcal{W}=(W_i,w_i{)}_{i\in I}$ for a Hilbert space $\mathcal{H}$ that provides that the sequence $(\overline{T(W_i)},v_i{)}_{i\in I}$ is a fusion frame sequence for $\mathcal{H}$, if we consider a suitable family of weights $\{v_i{\}}_{i\in I}$. This (sufficient) condition generalizes some previous work in the subject.

Lemma 1 (the error in the upper bound for the Moore-Penrose inverse of B). This error has been corrected in the final publication of the paper