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Pseudo-duals and closeness of continuous g-frames in Hilbert spaces | ||
| AUT Journal of Mathematics and Computing | ||
| دوره 7، شماره 1، فروردین 2026، صفحه 33-44 اصل مقاله (423.63 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2024.23279.1247 | ||
| نویسندگان | ||
| Morteza Mirzaee Azandaryani* ؛ Zeinab Javadi | ||
| Department of Mathematics, University of Qom, Qom, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Hilbert space؛ Continuous $g$-frame؛ Pseudo-dual؛ Approximate dual؛ The closeness of $g$-frames؛ The nearness of $g$-frames | ||
| مراجع | ||
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