On the Sum of g-Frames and Their Stability in Hilbert Spaces.

Since the finite sum of g-frames for a Hilbert space H may not be a g-frame for H, the sum of g-frames in Hilbert spaces are discussed in the present study. In fact, we first provide new sufficient conditions under which the sum of a g-frame and a g-Bessel sequence for a Hilbert space H is a g-frame for H. Subsequently, some results concerning the stability of g-frames for a Hilbert space H are obtained under some types of perturbations. [ABSTRACT FROM AUTHOR]