Perturbation and stability of operator frame for $En{d}_{\mathcal{A}}^{\ast }(\mathcal{H})$

Abstract

Frame theory is recently an active research area in mathematics, computer science, and engineering with many exciting applications in a variety of different fields. In this paper, we firstly give a characterization of operator frame for $En{d}_{\mathcal{A}}^{\ast }(\mathcal{H})$ and $K$-operator frames for $En{d}_{\mathcal{A}}^{\ast }(\mathcal{H})$. Lastly we consider the stability of operator frame for $En{d}_{\mathcal{A}}^{\ast }(\mathcal{H})$ and $K$-operator frames for $En{d}_{\mathcal{A}}^{\ast }(\mathcal{H})$ under perturbation and we establish some results.