On perturbation of continuous frames in Hilbert C*-modules

Hadi Ghasemi; Tayebe Lal Shateri

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arXiv · 2305.12794

On perturbation of continuous frames in Hilbert C*-modules

Hadi Ghasemi·Tayebe Lal Shateri

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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.

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BibTeX RIS

Hadi Ghasemi, Tayebe Lal Shateri. 2023-05-22. On perturbation of continuous frames in Hilbert C*-modules. https://arxiv.org/abs/2305.12794

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