pseudo-duals and closeness of continuous g-frames in hilbert spaces

The paper deals with pseudo-duals of continuous g-frames and their characterizations in hilbert spaces. mainly, the pseudo-duals constructed by bounded operators inserted between the synthesis and analysis operators of the bessel mappings are considered. duals and approximate duals, which are two important classes of pseudo-duals, are also studied here. moreover, the concepts of closeness and nearness of continuous g-frames are focused and some of their properties are obtained. it is shown that there are close relationships between the closeness and nearness of g-frames and their approximate duals. also, the abovementioned concepts are related to the notions of partial equivalence, equivalent frames, and continuous riesz-type g-frames.