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

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-gfusion 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.