فهرست نشریات علمی دسترسی آزاد ایران

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 above-mentioned concepts are related to the notions of partial equivalence, equivalent frames, and continuous Riesz-type $g$-frames.