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On perturbation of continuous frames in Hilbert C *-modules

  • Hadi Ghasemi and Tayebe Lal Shateri EMAIL logo
Published/Copyright: February 20, 2024
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Georgian Mathematical Journal
From the journal Georgian Mathematical Journal Volume 31 Issue 5

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 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.

Keywords: continuous frame; Riesz bases; dual; perturbation
MSC 2020: 47A55; 42C15

References

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Received: 2023-06-20
Revised: 2023-08-01
Accepted: 2023-08-03
Published Online: 2024-02-20
Published in Print: 2024-10-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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  2. Numerical approaches for solution of hyperbolic difference equations on circle
  3. A note on b-generalized (α,β)-derivations in prime rings
  4. Analytic solution to functional differential equations via Bell’s polynomials
  5. Floquet theory and stability for a class of first order differential equations with delays
  6. Representations of a number in an arbitrary base with unbounded digits
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  9. On perturbation of continuous frames in Hilbert C *-modules
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  12. Busemann--Petty-type problem for μ-intersection bodies
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  17. On the correspondence between periodic solutions of differential and dynamic equations on periodic time scales
https://doi.org/10.1515/gmj-2023-2111
Keywords for this article
continuous frame; Riesz bases; dual; perturbation

Articles in the same Issue

  1. Frontmatter
  2. Numerical approaches for solution of hyperbolic difference equations on circle
  3. A note on b-generalized (α,β)-derivations in prime rings
  4. Analytic solution to functional differential equations via Bell’s polynomials
  5. Floquet theory and stability for a class of first order differential equations with delays
  6. Representations of a number in an arbitrary base with unbounded digits
  7. V_a -deformed free convolution and variance function
  8. Generalized essential spectra involving the class of g-g-Riesz operators
  9. On perturbation of continuous frames in Hilbert C *-modules
  10. Almost measurable functions on probability spaces
  11. On φ-u-S-flat modules and nonnil-u-S-injective modules
  12. Busemann--Petty-type problem for μ-intersection bodies
  13. On the representation of solution for the perturbed quasi-linear controlled neutral functional-differential equation with the discontinuous initial condition
  14. A generalization of Hardy’s inequality to infinite tensors
  15. A note on maximal estimate for an oscillatory operator
  16. Some summation theorems and transformations for hypergeometric functions of Kampé de Fériet and Srivastava
  17. On the correspondence between periodic solutions of differential and dynamic equations on periodic time scales
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