%0 Journal Article
%T Hermitian solutions to the system of operator equations $T_iX=U_i$
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Vaezpour, S.Mansour
%A Bakhtiari, Zahra
%D 2019
%\ 11/01/2019
%V 10
%N 1
%P 139-152
%! Hermitian solutions to the system of operator equations $T_iX=U_i$
%K Operator equation
%K Hermitian solution
%K Common solution
%K Existence of solution
%K Moore penrose inverse
%R 10.22075/ijnaa.2017.1475.1378
%X 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 $\sum_{i=1}{n}T_iX_i=U$.
%U https://ijnaa.semnan.ac.ir/article_4059_01638be695de3fa1c98b915e397bc3bf.pdf