On perturbation of continuous frames in Hilbert C*-modules

Abstract

In the present paper, we examine the perturbation of continuous frames and Riesz-type frames in Hilbert $C^*$-modules. We extend the Casazza-Christensen general perturbation theorem for Hilbert space frames to continuous frames in Hilbert $C^*$-modules. We obtain a necessary condition under which the perturbation of a Riesz-type frame of Hilbert $C^*$-modules remains to be a Riesz-type frame. Also, we examine the effect of duality on the perturbation of continuous frames in Hilbert $C^*$-modules, and we prove if the operator frame of a continuous frame $F$ is near to the combination of the synthesis operator of a continuous Bessel mapping $G$ and the analysis operator of $F$, then $G$ is a continuous frame.