Characterizations of (near) exact g-frames, g-Riesz bases, and Besselian g-frames

In this paper, we use a new general sequence corresponding to a g-Bessel sequence {Lambda(j) : j is an element of J} to characterize that {Lambda(j) : j is an element of J} are l(2)({V-j} j is an element of J)-linear independent, g-complete and a g-frame. We also use {Lambda j : j is an element of J} and the refinement {Gamma(ij)Lambda(i) : i is an element of I, j is an element of J(i)} to characterize each other to be (near) exact g-frames or g-Riesz bases. Finally, we give several constructions and an equivalent characterization of Besselian g-frames and near exact g-frames.