Generalized fusion frames in Hilbert spaces

Abstract: After introducing g-frames and fusion frames by Sun and Casazza, combining these frames together is an interesting topic for research. In this paper, we introduce the generalized fusion frames or g-fusion frames for Hilbert spaces and give characterizations of these frames from the viewpoint of closed range and g-fusion frame sequences. Also, the canonical dual g-fusion frames are presented and we introduce Parseval g-fusion frames.