ON GENERALIZED WEAVING FRAMES IN HILBERT SPACES

Generalized frames (in short, g-frames) are a natural generalization of standard frames in separable Hilbert spaces. Motivated by the concept of weaving frames in separable Hilbert spaces by [1] in the context of distributed signal processing, we study weaving properties of g-frames. Firstly, we present necessary and sufficient conditions for weaving g-frames in Hilbert spaces. We extend some results of [1, 6] regarding conversion of standard weaving frames to g-weaving frames. Some Paley-Wiener type perturbation results for weaving g-frames are obtained. Finally, we give necessary and sufficient conditions for weaving g-Riesz bases.