English

On perturbation of continuous frames in Hilbert C*-modules

Functional Analysis 2023-05-23 v1

Abstract

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

Keywords

Cite

@article{arxiv.2305.12794,
  title  = {On perturbation of continuous frames in Hilbert C*-modules},
  author = {Hadi Ghasemi and Tayebe Lal Shateri},
  journal= {arXiv preprint arXiv:2305.12794},
  year   = {2023}
}

Comments

arXiv admin note: text overlap with arXiv:2302.13554, arXiv:2208.06799

R2 v1 2026-06-28T10:41:02.731Z