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Hilbert–Schmidt Frames: Duality, Weaving and Stability | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 13، دوره 11، شماره 1، تیر 2020، صفحه 159-173 اصل مقاله (166.31 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.4251 | ||
| نویسندگان | ||
| Mehdi Choubin* 1؛ Mohammadbagher Ghaemi2؛ Gwang Hui Kim3 | ||
| 1Department of Mathematics, Velayat University, Iranshahr, Iran | ||
| 2Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran | ||
| 3Department of Mathematics, Kangnam University, Yongin, Gyeonggi, 16979, Republic of Korea | ||
| تاریخ دریافت: 11 اسفند 1397، تاریخ بازنگری: 22 آبان 1398، تاریخ پذیرش: 13 دی 1398 | ||
| چکیده | ||
| In this paper, we give some sufficient conditions under which perturbations preserve Hilbert-Schmidt frames. Also show that the canonical dual of a perturbed Hilbert-Schmidt frame is a perturbation of the canonical dual (alternative dual respectively) of the original Hilbert-Schmidt frame and discuss best approximation in the set of all dual Hilbert-Schmidt frames. Next, we apply the woven principle to Hilbert-Schmidt frames and study the stability of weaving Hilbert-Schmidt frames under perturbations. Finally, we present sufficient conditions under which perturbations preserve weaving Hilbert-Schmidt frames and weaving dual Hilbert-Schmidt frames. | ||
| کلیدواژه‌ها | ||
| Hilbert-Schmidt frames؛ Weaving frames؛ Dual frames؛ Perturbation | ||
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