Standard g-Bessel sequences and K-g-frames in Hilbert $C^{\ast}$-modules | ||
| AUT Journal of Mathematics and Computing | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از 17 اردیبهشت 1405 | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2025.24558.1438 | ||
| نویسندگان | ||
| Fatemeh Zamani Mirarkoulaei1؛ Morteza Mirzaee Azandaryani* 2 | ||
| 1Department of Mathematics, Kharazmi University, Tehran, Iran | ||
| 2Department of Mathematics, University of Qom, Qom, Iran | ||
| چکیده | ||
| In the present paper, we obtain some necessary, sufficient and equivalent conditions for some special sequences in a Hilbert $C^{\ast}$-module to constitute a standard g-Bessel sequence or a K-g-frame, where K is an adjointable operator on the underlying Hilbert $C^{\ast}$-module. Mainly, it is shown that standard g-Bessel sequences and K-g-frames are stable under the different kinds of perturbations. Then, as a special kind of K-duals for a standard g-frame, its $\alpha$-duals are considered and characterized ($\alpha$ is an integer). Moreover, we get some conditions under which standard g-Bessel sequences, K-g-frames and $\alpha$-duals are preserved under the action of adjointable operators. | ||
| کلیدواژهها | ||
| Hilbert $C^*$-module؛ g-Bessel sequence؛ K-g-frame؛ $\alpha$-dual؛ Stability | ||
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آمار تعداد مشاهده مقاله: 187 |
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