Affiliation:
1. Department of Mathematics and Computer Sciences , [ 185150]Hakim Sabzevari University, Sabzevar , Iran
Abstract
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.
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