English

Operator frame for $Hom_{\mathcal{A}}^{\ast}(\mathcal{X})$

Functional Analysis 2022-12-15 v1

Abstract

The concept of operator frame can be considered as a generalization of frame. Firstly, we introduce the notion of operator frame for the set of all adjointable operators HomA(X)Hom_{\mathcal{A}}^{\ast}(\mathcal{X}) on a Hilbert pro-CC^{\ast}-module X.\mathcal{X}. The analysis operator, the synthesis operator and the frame operator are presented. Secondly, we study the stability of operator frame under small perturbations. We also study the tensor product of operator frame for Hilbert pro-CC^{\ast}-modules. Finally, we establish its dual and some properties.

Keywords

Cite

@article{arxiv.2212.07004,
  title  = {Operator frame for $Hom_{\mathcal{A}}^{\ast}(\mathcal{X})$},
  author = {Roumaissae Eljazzar and Mohamed Rossafi and Choonkil Park},
  journal= {arXiv preprint arXiv:2212.07004},
  year   = {2022}
}

Comments

arXiv admin note: text overlap with arXiv:2111.09835

R2 v1 2026-06-28T07:33:35.820Z