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

TL;DR

This paper characterizes operator frames and K-operator frames in a mathematical setting and investigates their stability under perturbations, contributing to the theoretical understanding of frame stability in operator theory.

Contribution

It provides new characterizations of operator frames and K-operator frames in $End_{\\mathcal{A}}^{\ ext{*}}(\\\mathcal{H})$ and analyzes their stability under perturbations.

Findings

Characterization of operator frames in $End_{\mathcal{A}}^{*}(\mathcal{H})$

Characterization of K-operator frames in $End_{\mathcal{A}}^{*}(\mathcal{H})$

Stability results for operator frames under perturbation

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 $End_{\mathcal{A}}^{\ast}(\mathcal{H})$ and $K$-operator frames for $End_{\mathcal{A}}^{\ast}(\mathcal{H})$. Lastly we consider the stability of operator frame for $End_{\mathcal{A}}^{\ast}(\mathcal{H})$ and $K$-operator frames for $End_{\mathcal{A}}^{\ast}(\mathcal{H})$ under perturbation and we establish some results.