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 * {C^{*}} -modules. We extend the Casazza–Christensen general perturbation theorem for Hilbert space frames to continuous frames in Hilbert C * {C^{*}} -modules. We obtain a necessary condition under which the perturbation of a Riesz-type frame of Hilbert C * {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 * {C^{*}} -modules, and we prove that 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.