The Sum Two of Hermitian Operators Ai=Ti+Mi for Solving the Equations{Ai X=Ui },i=1,2

Abstract

In this work we study a new class of equations (Ti+Mi)X=Ui, i=1,2 including the sum two of Hermitian operatorsTi and Mi , i=1,2, concerning the kind of spaces are Hilbert. The existence of joint Hermitian solutions to summing two equations of operators has been found under both necessary and sufficient conditions. The n*1 block's Moore-Penrose inverse of summing two matrix of operators has been studied. Therefore, we present Hermitian solutions of the two equations of operators (Ti+Mi)X(Qi+mi)=Ui, i=1,2 with finding of it’s the necessary and sufficient conditions.