A note on perturbations of Fusion Frames

TL;DR

This paper explores how certain operators affect fusion frames in Hilbert spaces, providing conditions under which the transformed sequence remains a fusion frame sequence, thus generalizing previous results.

Contribution

It introduces a sufficient condition relating closed range operators and fusion frames that extends prior work in the field.

Findings

Provides a new sufficient condition for fusion frame sequences under operator perturbations

Generalizes previous results on fusion frame stability

Enhances understanding of operator effects on 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.