Weaving g-fusion frames in Hilbert spaces

Fusion frames, one of the important frame extensions, introduced by Casazza and Kutyniok, Bemros et al. are able to transform the except of weaving from Gabor frames to frame theory; thus weaving frames.In this paper, we generalize the weaving fusion frames and study them from the viewpoint of the finite and infinite dimensional Hilbert spaces.Also, we introduce weakly g-fusion woven frame and show that they are equivalent with the weaving g-fusion frames.