Hermitian solutions to the system of operator equations T_iX=U_i.

Document Type: Research Paper

Authors

1 Amirkabir University of Technology (Tehran Polytechnic)

2 Department of Mathematics, Payam e Nour University, Tehran, Iran

Abstract

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

Keywords