Abstract:

The notion of disjointness of frames in Hilbert spaces was firstly introduced by Han and Larson, it is closely related with super frames in Hilbert spaces, and plays an important role in construction of super frames and frames. G-frames is a generalization of frames in Hilbert spaces. In this paper, we establish characterization of disjointness of g-frames, strong disjointness of g-frames and weak disjointness of g-frames in terms of super g-frames; With the results obtained, we give different proof method of the known theorem; We obtain the relation between strongly disjoint and weakly disjoint of dual g-frames; Finally, we use strong disjointness of g-frames to construct (super) dual g-frames, which cover the results obtained by other authors.

Key words: Generalized frames, Dual generalized frame, Disjointness