TY - JOUR
ID - 4059
TI - Hermitian solutions to the system of operator equations $T_iX=U_i$
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Vaezpour, S.Mansour
AU - Bakhtiari, Zahra
AD - Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
AD - Department of Mathematics, Payame Nour University, Tehran, Iran
Y1 - 2019
PY - 2019
VL - 10
IS - 1
SP - 139
EP - 152
KW - Operator equation
KW - Hermitian solution
KW - Common solution
KW - Existence of solution
KW - Moore penrose inverse
DO - 10.22075/ijnaa.2017.1475.1378
N2 - 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 $\sum_{i=1}{n}T_iX_i=U$.
UR - https://ijnaa.semnan.ac.ir/article_4059.html
L1 - https://ijnaa.semnan.ac.ir/article_4059_01638be695de3fa1c98b915e397bc3bf.pdf
ER -