Author/Authors :
Bakhtiari, Zahra Department of Mathematics - Payame Noor University, Tehran, Iran , Vaezpour, S. Mansour Department of Mathematics and Computer Science - Amirkabir University of Technology, Hafez Ave., Tehran, Iran , Ebadian, Ali Department of Mathematics - Payame Noor University, Tehran, Iran
Abstract :
In this article we consider the system of operator equations TiX = Ui for i = 1; 2; 3; :::; n, between
Hilbert spaces 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✖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 sufficient conditions for the existence of common Hermitian solutions to the system of operator
equations TiXVi = Ui, for i = 1; 2; 3; :::; n and also present the necessary conditions for solvability of
the equation Σn i=1 TiXi = U.
Keywords :
Moore Penrose inverse , Existence of solution , Common solution , Hermitian solution , Operator equation
