A note on perturbations of Fusion Frames

M. Ruiz; P. Calderón

A note on perturbations of Fusion Frames

Functional Analysis 2022-03-10 v2

Authors: M. Ruiz , P. Calderón

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.

Keywords

frame theory operator theory on hilbert spaces numerical range

Cite

@article{arxiv.1709.06872,
  title  = {A note on perturbations of Fusion Frames},
  author = {M. Ruiz and P. Calderón},
  journal= {arXiv preprint arXiv:1709.06872},
  year   = {2022}
}

Comments

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

A note on perturbations of Fusion Frames

Abstract

Keywords

Cite

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