Hermitian solutions to the system of operator equations T_iX=U_i.
S. M. Vaezpour, Zahra Bakhtiari · International journal of nonlinear analysis and applications · 2019
In this article we consider the system of operator equations T_iX=U_i for i=1,2,...,n and give necessary and suffcient 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 ncross 1 block operator matrix and. then give the general form of common Hermitian solutions to this system of equations. Cosequently, we give the necessary and sffcient conditions for the existence of common Hermitian solutions to the system of operator equati and also present the necessary conditions for solvability of the equation sum_{i=1}{n}T_iX_i=U