(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
In Hilbert spaces, K-g-frames are an advanced version of g-frames that enable the reconstruction of objects from the range of a bounded linear operator K. This research investigates K-g-frames in Hilbert space. Firstly, using the g-preframe operators, we characterize the dual K-g-Bessel sequence of a K-g frame. We provide additional requirements that must be met for the sum of a given K-g-frame and its dual K-g-Bessel sequence to be a K-g-frame. At the end of this paper, we present the concept of K-g-orthonormal bases and explain their link to g-orthonormal bases in Hilbert space. We also provide an alternative definition of K-g-Riesz bases using K-g-orthonormal bases. This gives a better understanding of the concept.