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Hermitian solutions to the system of operator equations $T_iX=U_i$ | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 13، دوره 10، شماره 1، بهمن 2019، صفحه 139-152 اصل مقاله (435.12 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2017.1475.1378 | ||
| نویسندگان | ||
| S.Mansour Vaezpour* 1؛ Zahra Bakhtiari2 | ||
| 1Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran | ||
| 2Department of Mathematics, Payame Nour University, Tehran, Iran | ||
| تاریخ دریافت: 07 دی 1396، تاریخ بازنگری: 23 خرداد 1397، تاریخ پذیرش: 09 تیر 1397 | ||
| چکیده | ||
| In this article, we consider the system of operator equations $T_iX=U_i$ for $i=1,2,...,n$ and give necessary and sufficient conditions for the existence of common Hermitian solutions to this system of operator equations for arbitrary operators without the closedness condition. Also, we study the Moore-Penrose inverse of a $n\times 1$ block operator matrix and then give the general form of common Hermitian solutions to this system of equations. Consequently, we give the necessary and sufficient conditions for the existence of common Hermitian solutions to the system of an operator equation and also present the necessary conditions for the solvability of the equation $\sum_{i=1}{n}T_iX_i=U$. | ||
| کلیدواژه‌ها | ||
| Operator equation؛ Hermitian solution؛ Common solution؛ Existence of solution؛ Moore penrose inverse | ||
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