Approximate Oblique Dual g-Frames for Closed Subspaces of Hilbert Spaces

In this paper, we first introduce the notion of approximate oblique dual g-frames for closed subspaces in Hilbert spaces and give a characterization. Then we give its interpretation in the setting of signal processing where the signals are considered as elements in a Hilbert space under certain requirements. We extend some important properties of approximate dual g-frames to oblique setting. Finally, we construct approximate oblique duals of g-frames for a closed subspace and give the formula. Moreover, we prove that if two g-frames for a closed subspace are close to each other, each oblique dual of any of them is an approximate oblique dual of the other.