Perturbation and Stability of Continuous Operator Frames in Hilbert $C^{\ast}$-Modules

TL;DR

This paper investigates the stability of continuous operator frames and K-operator frames within Hilbert C*-modules, extending classical frame theory to a more general algebraic setting and analyzing their perturbation resilience.

Contribution

It introduces new stability results for continuous operator frames and K-operator frames in Hilbert C*-modules, expanding the understanding of their robustness under perturbations.

Findings

Established stability properties of continuous operator frames

Analyzed perturbation effects on K-operator frames

Extended frame theory to Hilbert C*-modules

Abstract

Frame Theory has a great revolution in recent years. This Theory have been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. In this paper we consider the stability of continuous operator frame and continuous $K$-operator frames in Hilbert $C^{\ast}$-Modules under perturbation and we establish some properties