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

Sanae Touaiher, Maryam G. Alshehri () and Mohamed Rossafi
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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

Mathematics, 2025, vol. 13, issue 22, 1-13

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.

Keywords: Hilbert C *-module; fusion frame; generalized fusion frame; Cartesian product; perturbation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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