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K -g-Fusion Frames on Cartesian Products of Two Hilbert C *-Modules

Author

Listed:
  • Sanae Touaiher

    (Laboratory Analysis, Geometry and Applications, Faculty of Science, University of Ibn Tofail, P.O. Box 133, Kenitra 14000, Morocco)

  • Maryam G. Alshehri

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

  • Mohamed Rossafi

    (Laboratory Analysis, Geometry and Applications, Higher School of Education and Training, University of Ibn Tofail, P.O. Box 242, Kenitra 14000, Morocco)

Abstract

In this paper, we introduce and investigate the concept of K -g-fusion frames in the Cartesian product of two Hilbert C * -modules over the same unital C * -algebra. Our main result establishes that the Cartesian product of two K -g-fusion frames remains a K -g-fusion frame for the direct-sum module. We give explicit formulae for the associated synthesis, analysis, and frame operators and prove natural relations (direct-sum decomposition of the frame operator). Furthermore, we prove a perturbation theorem showing that small perturbations of the component families, measured in the operator or norm sense, still yield a K -g-fusion frame for the product module, with explicit new frame bounds obtained.

Suggested Citation

  • Sanae Touaiher & Maryam G. Alshehri & Mohamed Rossafi, 2025. "K -g-Fusion Frames on Cartesian Products of Two Hilbert C *-Modules," Mathematics, MDPI, vol. 13(22), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:22:p:3576-:d:1789714
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