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.
Mirzaee Azandaryani, M., & Javadi, Z. (2024). Pseudo-duals and closeness of continuous $g$-frames in Hilbert spaces. AUT Journal of Mathematics and Computing, (), -. doi: 10.22060/ajmc.2024.23279.1247
MLA
Morteza Mirzaee Azandaryani; Zeinab Javadi. "Pseudo-duals and closeness of continuous $g$-frames in Hilbert spaces". AUT Journal of Mathematics and Computing, , , 2024, -. doi: 10.22060/ajmc.2024.23279.1247
HARVARD
Mirzaee Azandaryani, M., Javadi, Z. (2024). 'Pseudo-duals and closeness of continuous $g$-frames in Hilbert spaces', AUT Journal of Mathematics and Computing, (), pp. -. doi: 10.22060/ajmc.2024.23279.1247
VANCOUVER
Mirzaee Azandaryani, M., Javadi, Z. Pseudo-duals and closeness of continuous $g$-frames in Hilbert spaces. AUT Journal of Mathematics and Computing, 2024; (): -. doi: 10.22060/ajmc.2024.23279.1247
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