Dual G-frames Research Articles

Fusion frames and g-frames

Fusion frames and g-frames were considered recently as generalizations of frames in Hilbert spaces, in this paper we generalize some of the known results in frame theory to fusion frames and g-frames. We obtain new g-frames by considering g-frames for its components. We also obtain some results about alternate dual g-frames, excess of g-frames and stability of g-frames under small perturbations.

Stability of g-frames

g-Frames are natural generalizations of frames which cover many other recent generalizations of frames, e.g., bounded quasi-projectors, frames of subspaces, outer frames, oblique frames, pseudo-frames and a class of time-frequency localization operators. Moreover, it is known that g-frames are equivalent to stable space splittings. In this paper, we study the stability of g-frames. We first present some properties for g-Bessel sequences. Then we prove that g-frames are stable under small perturbations. We also study the stability of dual g-frames.