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October 12, 2025Open Access

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

Puntos clave

The key finding shows that the Cartesian product of two K-g-fusion frames continues to form a K-g-fusion frame.
Explicit formulae for synthesis and analysis operators were derived, proving fundamental relationships, including direct-sum decompositions.
The perturbation theorem indicates that small adjustments in the families still yield K-g-fusion frames with new frame bounds.
The study emphasizes the stability of K-g-fusion frames under perturbations within the context of direct-sum modules.

Resumen

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.

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